UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT

INVESTMENT COMPANIES

Investment Company Act file number: 811-02688

Name and address of agent for service: John M. Perlowski, Chief Executive Officer, BlackRock Municipal Bond Fund, Inc., 55 East 52^nd Street, New York, NY 10055

Registrant’s telephone number, including area code: (800) 441-7762

Date of fiscal year end: 06/30/2021

Date of reporting period: 06/30/2021

(a) The Report to Shareholders is attached herewith.

BlackRock Multi-State Municipal Series Trust

BlackRock Municipal Bond Fund, Inc.

Table of Contents

Investment Objective

BlackRock New York Municipal Opportunities Fund’s (the “Fund”) investment objective is to provide shareholders with income exempt from Federal income tax and New York State and New York City personal income taxes.

Portfolio Management Commentary

How did the Fund perform?

For the 12-month period ended June 30, 2021, the Fund outperformed the primary benchmark, the S&P^® Municipal Bond Index, and the secondary benchmark, the S&P^® New York Municipal Bond Index. The following discussion of relative performance pertains to the Fund’s secondary benchmark, the S&P^® New York Municipal Bond Index.

What factors influenced performance?

Despite rising U.S. Treasury yields, municipal bonds delivered strong returns in the past 12 months. (Prices and yields move in opposite directions.) When the period began in July 2020, the market was still suffering from the dislocations caused by COVID-19. However, tax-exempt bonds gradually climbed off of their pandemic-driven lows due to the release of multiple coronavirus vaccines, better-than-expected growth, improving municipal finances and robust investor demand. The prospect of substantial fiscal stimulus and higher taxes were additional tailwinds for the market. These factors led to a decline in yield spreads versus U.S. Treasuries, fueling gains for municipal debt. New York municipal bonds modestly outpaced the national index. The state, which experienced an above-average impact from the coronavirus-induced downturn, has outperformed in the subsequent recovery.

Both security selection and asset allocation contributed to the Fund’s positive performance.

With respect to allocation, the Fund benefited from its overweight position in lower-rated bonds due to the category’s strong outperformance relative to higher-quality debt. Holdings in the tobacco sector also aided results, as did an overweight in long-term bonds.

In terms of selection, the best results came from the state tax-backed and utilities sectors. In both cases, the relative strength largely stemmed from holdings in Puerto Rico.

The Fund’s use of U.S. Treasury futures to manage interest-rate risk further helped performance given that Treasury yields rose even as municipals gained ground.

The Fund experienced a small, negative impact from security selection in the transportation sector. The portfolio’s cash position, while limited, nonetheless detracted somewhat at a time of positive returns for the market as a whole.

Describe recent portfolio activity.

Portfolio activity was largely driven by the investment adviser’s efforts to put cash to work by capitalizing on relative valuations and the opportunities created by new issuance. The Fund increased its allocations to lower-quality securities and Puerto Rico and reduced its cash position marginally as market liquidity returned. In terms of maturity exposure, the investment adviser decreased the Fund’s weightings in securities with maturities of 20 years and above and increased its weighting in those with maturities of less than 20 years.

Describe portfolio positioning at period end.

The Fund ended the period with an overweight position in longer-maturity bonds, largely those in the 15- to 20-year area. Additionally, the Fund maintained an overweight in lower-quality issues (those rated A and below). The Fund’s duration was below the benchmark at the end of the period, but to a lesser extent than it was at the beginning of the period.

The views expressed reflect the opinions of BlackRock as of the date of this report and are subject to change based on changes in market, economic or other conditions. These views are not intended to be a forecast of future events and are no guarantee of future results.

TOTAL RETURN BASED ON A $10,000 INVESTMENT

Performance Summary for the Period Ended June 30, 2021

N/A — Not applicable as the share class and index do not have a sales charge.

Past performance is not an indication of future results.

Performance results may include adjustments made for financial reporting purposes in accordance with U.S. generally accepted accounting principles.

Expense Example

Expense Example (continued)

Portfolio Information

Investment Objective

BlackRock High Yield Municipal Fund’s (the “Fund”) investment objective is to provide shareholders with as high a level of income exempt from Federal income taxes as is consistent with the investment policies of the Fund.

Portfolio Management Commentary

How did the Fund perform?

For the 12-month period ended June 30, 2021, the Fund outperformed both its primary benchmark, the S&P^® Municipal Bond Index, and its secondary benchmark, the Custom High Yield Index. The following discussion of relative performance pertains to the Custom High Yield Index.

What factors influenced performance?

Despite rising U.S. Treasury yields, municipal bonds delivered healthy gains in the past 12 months. (Prices and yields move in opposite directions.) When the period began in July 2020, the market was still suffering from the dislocations caused by COVID-19. However, tax-exempt bonds gradually climbed off of their pandemic-driven lows thanks to the release of multiple coronavirus vaccines, better-than-expected growth, improving municipal finances and robust investor demand. The prospect of substantial fiscal stimulus and higher taxes were additional tailwinds for the market. These factors led to a decline in yield spreads versus U.S. Treasuries, fueling gains for municipal debt. High-yield bonds, which benefited from investors’ appetite for both risk and yield, were especially strong performers.

Positions in longer-dated securities with maturities of 20 years and above contributed to Fund performance, as did holdings in bonds on the lower end of the investment-grade spectrum. At the sector level, the largest contributions came from utilities, state tax-backed, education and corporate-related debt. Investments in distressed obligations issued in Puerto Rico and elsewhere strongly outperformed the broader high yield category, further helping performance.

The Fund’s underweight in BB rated securities detracted from performance. Underweight positions in the five- to 20-year maturity range and the local tax-backed sector also weighed on relative performance. In the latter part of the period, a cash position hurt results by preventing the Fund from benefiting from the market’s positive return in this time. Despite the modest drag from holding cash, the portfolio remained positioned in an aggressive enough manner to offset much of the effect. The Fund also sought to manage interest-rate risk using U.S. Treasury futures late in the period, which was a very small detractor.

Describe recent portfolio activity.

The Fund adopted a more aggressive posture with respect to credit risk in late 2020. Later, the uptick in yields in the first quarter of 2021 created opportunities to capture better value in both investment-grade and non-investment grade securities. Elevated cash reserves provided the latitude to satisfy much of the shareholder redemptions that coincided with the rise in yields, eliminating the need to sell into weakness and facilitating the investment adviser’s ability to capitalize on the opportunity.

As the period progressed, the investment adviser turned its efforts to unearthing bespoke opportunities where it could structure transactions to its own liking and purchase them in their entirety, thereby avoiding the need to compete for bonds in what has become a frothy, risk-loving public market. Recent opportunities included investments in the senior living and charter school sectors.

Describe portfolio positioning at period end.

The Fund at times held an elevated cash balance during the period. This was in part a reflection of elevated inflows into the Fund, as well as the investment adviser’s desire to maintain sufficient liquidity in the event market conditions become less favorable. With that said, the portfolio remained positioned for a continuation of the positive investment environment. The portfolio’s duration (interest-rate sensitivity) was modestly higher than that of the benchmark.

Despite stretched valuations on both an absolute and relative basis, the investment adviser saw the combination of low supply and robust demand as a source of ongoing support for municipal bonds. Nonetheless, the investment adviser sought to offset the potential for increased market volatility by trimming some of the Fund’s more aggressive positions and maintaining its risk-management strategy with respect to interest rates.

The views expressed reflect the opinions of BlackRock as of the date of this report and are subject to change based on changes in market, economic or other conditions. These views are not intended to be a forecast of future events and are no guarantee of future results.

TOTAL RETURN BASED ON A $10,000 INVESTMENT

Performance Summary for the Period Ended June 30, 2021

N/A — Not applicable as the share class and index do not have a sales charge.

Past performance is not an indication of future results.

Performance results may include adjustments made for financial reporting purposes in accordance with U.S. generally accepted accounting principles.

Expense Example

Portfolio Information

Investment Objective

BlackRock National Municipal Fund’s (the “Fund”) investment objective is to provide shareholders with as high a level of income exempt from Federal income taxes as is consistent with the investment policies of the Fund.

Portfolio Management Commentary

How did the Fund perform?

For the 12-month period ended June 30, 2021, the Fund outperformed the primary benchmark, the S&P^® Municipal Bond Index. For the same period, the Fund’s Institutional and Class K Shares outperformed the secondary benchmark, the Custom National Index, while the Fund’s Service, Investor A and Investor C Shares underperformed. The following discussion of relative performance pertains to the Custom National Index.

What factors influenced performance?

Despite rising U.S. Treasury yields, municipal bonds delivered strong returns in the past 12 months. (Prices and yields move in opposite directions.) When the period began in July 2020, the market was still suffering the dislocations caused by COVID-19. However, tax-exempt bonds gradually climbed off of their pandemic-driven lows thanks to the release of multiple coronavirus vaccines, better-than-expected growth, improving municipal finances and robust investor demand. The prospect of substantial fiscal stimulus and higher taxes were additional tailwinds for the market. These factors led to a decline in yield spreads versus U.S. Treasuries, fueling impressive gains for municipal debt.

The Fund benefited from its holdings in longer-duration, longer-maturity securities. (Duration is a measure of interest rate sensitivity). The Fund’s use of U.S. Treasury futures to manage interest-rate risk also aided performance given that Treasury yields rose even as municipal bonds gained ground.

At the sector level, the Fund was helped by its positions in the health care, education, transportation, utilities and corporate-backed sectors. Positions in bonds with shorter call dates—a market segment that benefited from rising demand—also added value. (A call is when an issuer redeems a bond prior to its maturity date.) An allocation to high-yield bonds and lower-rated investment-grade securities—particularly in the tobacco sector—was a further plus, as investors were willing to move down in credit quality in order to earn higher income.

The Fund’s above-average cash position detracted from Fund performance given the rally in municipal bonds. The Fund’s allocations to state-tax backed and local-authority debt, which lagged the broader market, also detracted.

Describe recent portfolio activity.

The investment adviser continued to focus on constructing a balanced, higher-quality and income-oriented portfolio. The investment adviser maintained an elevated cash position to provide liquidity in the event that the coronavirus pandemic endangered the tax revenues of state and local municipalities. For most issuers, this threat did not in fact materialize. The investment adviser raised the Fund’s allocation to high-yield bonds from 10% to 12% on the belief that this segment offered a greater representation of attractively valued securities.

Describe portfolio positioning at period end.

The Fund had an average credit quality of AA-, up from A+ one year ago, and it held a 9.0% weighting in bonds subject to the alternative minimum tax. Duration stood at 6.0 years on June 30, 2021, in line with the benchmark. Leverage was 1.4% of assets, versus 5% at the beginning of the period. The portfolio was overweight in the health care and corporate-backed sectors, while its largest underweight was in the state tax-backed category.

The views expressed reflect the opinions of BlackRock as of the date of this report and are subject to change based on changes in market, economic or other conditions. These views are not intended to be a forecast of future events and are no guarantee of future results.

TOTAL RETURN BASED ON A $10,000 INVESTMENT

Performance Summary for the Period Ended June 30, 2021

N/A — Not applicable as the share class and index do not have a sales charge.

Past performance is not an indication of future results.

Performance results may include adjustments made for financial reporting purposes in accordance with U.S. generally accepted accounting principles.

Expense Example

Expense Example (continued)

Portfolio Information

Investment Objective

BlackRock Short-Term Municipal Fund’s (the “Fund”) investment objective is to provide shareholders with as high a level of income exempt from Federal income taxes as is consistent with the investment policies of the Fund.

Portfolio Management Commentary

How did the Fund perform?

For the 12-month period ended June 30, 2021, the Fund underperformed its primary benchmark, the S&P^® Municipal Bond Index, and its secondary benchmark, the S&P^® Limited Maturity Municipal Bond Index. The following discussion of relative performance pertains to the Fund’s secondary benchmark, the S&P^® Limited Maturity Municipal Bond Index.

What factors influenced performance?

Short-term municipal bonds delivered muted gains in the past 12 months. Although the improving outlook for state and local finances led to positive returns for municipal bonds, shorter-term issues—which are more sensitive to expectations regarding U.S. Federal Reserve policy—finished somewhat behind the broader market.

The Fund’s underperformance stemmed, in part, from an underweight in high-grade securities (those rated AAA and AA). At the sector level, underweights in pre-refunded issues, local tax-backed debt, education, transportation and utilities hurt results, as did an overweight in state tax-backed issues. An underweight in the four-year portion of the yield curve also pressured relative performance.

On the positive side, the Fund benefited from its overweights in A and BBB rated bonds. An overweight in the zero- to one-year part of the yield curve helped performance, as did an underweight in one- to three-year issues. At the sector level, overweight positions in health care, corporate-backed, housing and tobacco securities contributed positively to Fund performance.

Describe recent portfolio activity.

The Fed kept the Fed Funds rate near zero and pledged to use all of the tools at its disposal to keep the economy stable. In addition, Congress provided fiscal stimulus packages to support economic growth. With this as the backdrop, the investment adviser’s investment strategy initially focused on tactically positioning the Fund by increasing duration (interest-rate sensitivity) in anticipation of an extended period of low interest rates. However, this strategy became challenged as the Fund experienced large inflows, and new bond issuance—especially inside of four years—was limited. The investment adviser therefore increased its focus on the secondary market as a means of uncovering additional opportunities to help execute its strategy. The low-rate environment also prompted the investment adviser to search for compelling investments in lower-rated debt.

Supply-and-demand conditions remained favorable later in the period, but signs of rising inflation fostered concerns that the Fed may need to tighten policy. With yields near historical lows, the investment adviser became more cautious in adding longer-dated issues. The Fund used short-term, high-quality variable rate demand notes (“VRDNs”) as a low-risk investment alternative as it sought opportunities in longer-term debt. The Fund, after reducing its positions in VRDNs over the first nine months of the period, subsequently increased the allocation due to a large amount of bond holdings that matured. The Fund had an allocation of approximately 26% in VRDNs at the end of the period.

Describe portfolio positioning at period end.

At the end of June 30, 2021, the Fund held 47% of assets in securities maturing in less than a year and 14% in those with maturities of one to two years. The Fund’s weightings in the two- to three-year and three- to four-year portions of the curve were 27% and 12%, respectively. However, the investment adviser continued to look for specific opportunities in longer-dated securities.

The Fund’s maintained overweight positions in A and BBB rated debt and an underweight in AAA rated debt.

The views expressed reflect the opinions of BlackRock as of the date of this report and are subject to change based on changes in market, economic or other conditions. These views are not intended to be a forecast of future events and are no guarantee of future results.

TOTAL RETURN BASED ON A $10,000 INVESTMENT

Performance Summary for the Period Ended June 30, 2021

N/A — Not applicable as the share class and index do not have a sales charge.

Past performance is not an indication of future results.

Performance results may include adjustments made for financial reporting purposes in accordance with U.S. generally accepted accounting principles.

Expense Example

Portfolio Information

About Fund Performance

Institutional and Class K Shares are not subject to any sales charge. These shares bear no ongoing distribution or service fees and are available only to certain eligible investors. BlackRock High Yield Municipal Fund’s and BlackRock New York Municipal Opportunities Fund’s Class K Share performance shown prior to the Class K shares inception date of January 25, 2018 is that of the respective Fund’s Institutional Shares. BlackRock National Municipal Fund’s Class K Share performance shown prior to the Class K shares inception date of July 18, 2011 is that of Institutional Shares. The performance of each Fund’s Class K Shares would be substantially similar to Institutional Shares because Class K Shares and Institutional Shares invest in the same portfolio of securities and performance would only differ to the extent that Class K Shares and Institutional Shares have different expenses. The actual returns of Class K Shares would have been higher than those of the Institutional Shares because Class K Shares have lower expenses than the Institutional Shares. On the close of business on August 15, 2016, all of the issued and outstanding BlackRock Shares of BlackRock National Municipal Fund were redesignated as Class K Shares.

Service Shares (available only in BlackRock National Municipal Fund) are not subject to any sales charge. These shares are subject to a service fee of 0.25% per year (but no distribution fee) and are only available to certain eligible investors. Prior to July 18, 2011, Service Share performance results are those of the Institutional Shares restated to reflect Service Share fees.

Investor A Shares are subject to a maximum initial sales charge (front-end load) of 4.25% for all Funds except BlackRock Short-Term Municipal Fund, which incurs a 3.00% maximum initial sales charge, and all Funds incur a service fee of 0.25% per year (but no distribution fee). Certain redemptions of these shares may be subject to a contingent deferred sales charge (“CDSC”) where no initial sales charge was paid at the time of purchase. These shares are generally available through financial intermediaries.

Investor A1 Shares (available only in BlackRock Short-Term Municipal Fund and BlackRock New York Municipal Opportunities Fund) are subject to a maximum initial sales charge (front-end load) of 1.00% for BlackRock Short-Term Municipal Fund and 4.00% for BlackRock New York Municipal Opportunities Fund and a service fee of 0.10% per year (but no distribution fee). The maximum initial sales charge does not apply to current eligible investors of Investor A1 Shares of the Funds. These shares are only available for dividend and capital gain reinvestment by existing shareholders and for purchase by certain eligible employer-sponsored retirement plans. Certain redemptions of these shares may be subject to a CDSC where no initial sales charge was paid at the time of purchase. However, the CDSC does not apply to redemptions by certain employer-sponsored retirement plans or to redemptions of shares acquired through reinvestment of dividends and capital gains by existing shareholders.

Investor C Shares are subject to a 1.00% CDSC if redeemed within one year of purchase. In addition, these shares are subject to a distribution fee of 0.75% per year and a service fee of 0.25% per year. These shares are generally available through financial intermediaries. These shares automatically convert to Investor A Shares after approximately eight years.

Past performance is not an indication of future results. Financial markets have experienced extreme volatility and trading in many instruments has been disrupted. These circumstances may continue for an extended period of time, and may continue to affect adversely the value and liquidity of the Fund’s investments. As a result, current performance may be lower or higher than the performance data quoted. Refer to blackrock.com to obtain performance data current to the most recent month-end. Performance results do not reflect the deduction of taxes that a shareholder would pay on Fund distributions or the redemption of Fund shares. Figures shown in the performance tables assume reinvestment of all distributions, if any, at net asset value (“NAV”) on the ex-dividend date or payable date, as applicable. Investment return and principal value of shares will fluctuate so that shares, when redeemed, may be worth more or less than their original cost. Distributions paid to each class of shares will vary because of the different levels of service, distribution and transfer agency fees applicable to each class, which are deducted from the income available to be paid to shareholders.

BlackRock Advisors, LLC (the “Manager”), each Fund’s investment adviser, has contractually and/or voluntarily agreed to waive and/or reimburse a portion of each Fund’s expenses. Without such waiver(s) and/or reimbursement(s), each Fund’s performance would have been lower. With respect to each Fund’s voluntary waiver(s), if any, the Manager is under no obligation to waive and/or reimburse or to continue waiving and/or reimbursing its fees and such voluntary waiver(s) may be reduced or discontinued at any time. With respect to each Fund’s contractual waiver(s), if any, the Manager is under no obligation to continue waiving and/or reimbursing its fees after the applicable termination date of such agreement. See the Notes to Financial Statements for additional information on waivers and/or reimbursements.

The standardized 30-day yield includes the effects of any waivers and/or reimbursements. The unsubsidized 30-day yield excludes the effects of any waivers and/or reimbursements.

Disclosure of Expenses

Shareholders of each Fund may incur the following charges: (a) transactional expenses, such as sales charges; and (b) operating expenses, including investment advisory fees, service and distribution fees, including 12b-1 fees, acquired fund fees and expenses, and other fund expenses. The expense examples shown (which are based on a

Disclosure of Expenses  (continued)

hypothetical investment of $1,000 invested on January 1, 2021 and held through June 30, 2021) are intended to assist shareholders both in calculating expenses based on an investment in each Fund and in comparing these expenses with similar costs of investing in other mutual funds.

The expense examples provide information about actual account values and actual expenses. In order to estimate the expenses a shareholder paid during the period covered by this report, shareholders can divide their account value by $1,000 and then multiply the result by the number corresponding to their Fund and share class under the heading entitled “Expenses Paid During the Period.”

The expense examples also provide information about hypothetical account values and hypothetical expenses based on a Fund’s actual expense ratio and an assumed rate of return of 5% per year before expenses. In order to assist shareholders in comparing the ongoing expenses of investing in these Funds and other funds, compare the 5% hypothetical examples with the 5% hypothetical examples that appear in shareholder reports of other funds.

The expenses shown in the expense examples are intended to highlight shareholders’ ongoing costs only and do not reflect transactional expenses, such as sales charges, if any. Therefore, the hypothetical examples are useful in comparing ongoing expenses only, and will not help shareholders determine the relative total expenses of owning different funds. If these transactional expenses were included, shareholder expenses would have been higher.

The Benefits and Risks of Leveraging

The Funds may utilize leverage to seek to enhance returns and net asset value (“NAV”). However, there is no guarantee that these objectives can be achieved in all interest rate environments.

Each of BlackRock High Yield Municipal Fund, BlackRock New York Municipal Opportunities Fund and BlackRock National Municipal Fund may leverage its assets through the use of proceeds received in tender option bond (“TOB”) transactions, as described in the Notes to Financial Statements. In a TOB Trust transaction, each Fund transfers municipal bonds or other municipal securities into a special purpose entity (a “TOB Trust”). TOB investments generally provide each Fund with economic benefits in periods of declining short-term interest rates, but expose each Fund to risks during periods of rising short-term interest rates. Additionally, fluctuations in the market value of municipal bonds deposited into a TOB Trust may adversely affect each Fund’s NAV per share.

In general, the concept of leveraging is based on the premise that the financing cost of leverage, which is based on short-term interest rates, is normally lower than the income earned by each Fund on its longer-term portfolio investments purchased with the proceeds from leverage. To the extent that the total assets of each Fund (including the assets obtained from leverage) are invested in higher-yielding portfolio investments, the Fund’s shareholders benefit from the incremental net income.

The interest earned on securities purchased with the proceeds from leverage is distributed to the Funds’ shareholders, and the value of these portfolio holdings is reflected in each Fund’s per share NAV. However, in order to benefit shareholders, the return on assets purchased with leverage proceeds must exceed the ongoing costs associated with the leverage. If interest and other ongoing costs of leverage exceed a Fund’s return on assets purchased with leverage proceeds, income to shareholders is lower than if the Fund had not used leverage.

Furthermore, the value of each Fund’s portfolio investments generally varies inversely with the direction of long-term interest rates, although other factors can also influence the value of portfolio investments. As a result, changes in interest rates can influence each Fund’s NAV positively or negatively in addition to the impact on each Fund’s performance from leverage. Changes in the direction of interest rates are difficult to predict accurately, and there is no assurance that a Fund’s leveraging strategy will be successful.

The use of leverage also generally causes greater changes in each Fund’s NAV and dividend rates than comparable portfolios without leverage. In a declining market, leverage is likely to cause a greater decline in the NAV of a Fund’s shares than if the Fund was not leveraged. In addition, each Fund may be required to sell portfolio securities at inopportune times or at distressed values in order to comply with regulatory requirements applicable to the use of leverage or as required by the terms of the leverage instruments, which may cause the Funds to incur losses. The use of leverage may limit a Fund’s ability to invest in certain types of securities or use certain types of hedging strategies. Each Fund incurs expenses in connection with the use of leverage, all of which are borne by each Fund’s shareholders and may reduce income.

Derivative Financial Instruments

The Funds may invest in various derivative financial instruments. These instruments are used to obtain exposure to a security, commodity, index, market, and/or other assets without owning or taking physical custody of securities, commodities and/or other referenced assets or to manage market, equity, credit, interest rate, foreign currency exchange rate, commodity and/or other risks. Derivative financial instruments may give rise to a form of economic leverage and involve risks, including the imperfect correlation between the value of a derivative financial instrument and the underlying asset, possible default of the counterparty to the transaction or illiquidity of the instrument. The Funds’ successful use of a derivative financial instrument depends on the investment adviser’s ability to predict pertinent market movements accurately, which cannot be assured. The use of these instruments may result in losses greater than if they had not been used, may limit the amount of appreciation a Fund can realize on an investment and/or may result in lower distributions paid to shareholders. The Funds’ investments in these instruments, if any, are discussed in detail in the Notes to Financial Statements.