Exhibit 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Insteel Industries, Inc. (the “Company”) for the period ended April 1, 2023 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, H. O. Woltz III, President, Chief Executive Officer and Chairman of the Board of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

(1)         the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2)         the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ H.O. Woltz III

     H.O. Woltz III

     President, Chief Executive Officer and Chairman of the Board

     April 20, 2023