Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our reports dated October 29, 2026 with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of Insteel Industries Inc. on Form 10-K for the year ended October 3, 2026. We consent to the incorporation by reference of said reports in the Registration Statements of Insteel Industries Inc. on Forms S-8 (File No. 333-202128, File No. 333-236744, and File No. 333-284817).

/s/ Grant Thornton LLP

Charlotte, North Carolina

October 29, 2026