<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019e8514-58d5-71e1-a709-47ddfc86233b,g:efc25606-a1aa-4e78-b17b-c3619e8390a7-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:ck0000773674="http://www.americancentury.com/20260729" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.americancentury.com/20260729">
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/fnd-oef/2026" schemaLocation="https://xbrl.sec.gov/fnd/2026/fnd-oef-2026.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/oef-rr/2026" schemaLocation="https://xbrl.sec.gov/oef/2026/oef-rr-2026.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0000773674-20260729_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0000773674-20260729_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0000773674-20260729_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="ck0000773674_S000005965Member" abstract="true" name="S000005965Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_AmericanCenturyGovernmentIncomeTrustMember" abstract="true" name="AmericanCenturyGovernmentIncomeTrustMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016429Member" abstract="true" name="C000016429Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_S000005966Member" abstract="true" name="S000005966Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016430Member" abstract="true" name="C000016430Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000189731Member" abstract="true" name="C000189731Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016431Member" abstract="true" name="C000016431Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088034Member" abstract="true" name="C000088034Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000051003Member" abstract="true" name="C000051003Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000051002Member" abstract="true" name="C000051002Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_InterestRateRisksMember" abstract="true" name="InterestRateRisksMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_PrepaymentAndExtensionRiskMember" abstract="true" name="PrepaymentAndExtensionRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_DerivativesRiskMember" abstract="true" name="DerivativesRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_MarketRiskMember" abstract="true" name="MarketRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_RedemptionRiskMember" abstract="true" name="RedemptionRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BloombergU.S.AggregateBondIndexMember" abstract="true" name="BloombergU.S.AggregateBondIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BloombergUSGNMAIndexMember" abstract="true" name="BloombergUSGNMAIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_S000005968Member" abstract="true" name="S000005968Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016435Member" abstract="true" name="C000016435Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000189732Member" abstract="true" name="C000189732Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016436Member" abstract="true" name="C000016436Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088036Member" abstract="true" name="C000088036Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088037Member" abstract="true" name="C000088037Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088035Member" abstract="true" name="C000088035Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BloombergUSGovernmentMBSIndexMember" abstract="true" name="BloombergUSGovernmentMBSIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_S000005970Member" abstract="true" name="S000005970Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016440Member" abstract="true" name="C000016440Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000189733Member" abstract="true" name="C000189733Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016441Member" abstract="true" name="C000016441Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088041Member" abstract="true" name="C000088041Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088042Member" abstract="true" name="C000088042Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088040Member" abstract="true" name="C000088040Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BloombergUS13YearGovernmentBondIndexMember" abstract="true" name="BloombergUS13YearGovernmentBondIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_S000005969Member" abstract="true" name="S000005969Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016437Member" abstract="true" name="C000016437Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000181796Member" abstract="true" name="C000181796Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000181797Member" abstract="true" name="C000181797Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016438Member" abstract="true" name="C000016438Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088038Member" abstract="true" name="C000088038Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000088039Member" abstract="true" name="C000088039Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000016439Member" abstract="true" name="C000016439Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000191079Member" abstract="true" name="C000191079Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_C000191080Member" abstract="true" name="C000191080Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_InflationIndexedBondsRiskMember" abstract="true" name="InflationIndexedBondsRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_CreditRisksMember" abstract="true" name="CreditRisksMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_HighYieldRiskMember" abstract="true" name="HighYieldRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_LiquidityRiskMember" abstract="true" name="LiquidityRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_ForeignSecuritiesRiskMember" abstract="true" name="ForeignSecuritiesRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BankLoanRiskMember" abstract="true" name="BankLoanRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_CollateralizedObligationsRiskMember" abstract="true" name="CollateralizedObligationsRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_WhenIssuedAndForwardCommitmentRiskMember" abstract="true" name="WhenIssuedAndForwardCommitmentRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_MortgageAndAssetBackedSecuritiesRiskMember" abstract="true" name="MortgageAndAssetBackedSecuritiesRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_MortgageDollarRollsRiskMember" abstract="true" name="MortgageDollarRollsRiskMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="ck0000773674_BloombergUSTreasuryInflationProtectedSecuritiesTIPSIndexMember" abstract="true" name="BloombergUSTreasuryInflationProtectedSecuritiesTIPSIndexMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
</xs:schema>
