Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our reports dated October 29, 2020 with respect to the consolidated financial statements, schedule, 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, 2020. We consent to the incorporation by reference of said reports in the Registration Statements of Insteel Industries, Inc. on Forms S-8 (File No. 333-236744, File No. 333-48011, File No. 333-30934, File No. 333-123325, File No. 333-179670 and File No. 333-202128).

/s/ Grant Thornton LLP

Charlotte, North Carolina

October 29, 2020