EXHIBIT 32.1

Certifications by Chief Executive Officer (who serves as Principal Executive Officer) and Senior Vice President and Chief Financial Officer (who serves as Principal Financial Officer) 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 of Abercrombie & Fitch Co. (the “Corporation”) on Form 10-Q for the quarterly period ended August 4, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned Fran Horowitz, Chief Executive Officer of the Corporation (serving as Principal Executive Officer of the Corporation) and Scott Lipesky, Senior Vice President and Chief Financial Officer of the Corporation (serving as Principal Financial Officer of the Corporation), certify, pursuant to Section 1350 of Chapter 63 of Title 18 of the United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

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

(2) The information contained in the Report fairly presents, in all material respects, the consolidated financial condition and results of operations of the Corporation and its subsidiaries.

/s/ Fran Horowitz	/s/ Scott Lipesky
Fran Horowitz Chief Executive Officer (Principal Executive Officer)	Scott Lipesky Senior Vice President and Chief Financial Officer (Principal Financial Officer)
Date: September 10, 2018	Date: September 10, 2018

* These certifications are being furnished as required by Rule 13a-14(b) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and Section 1350 of Chapter 63 of Title 18 of the United States Code, and shall not be deemed “filed” for purposes of Section 18 of the Exchange Act or otherwise subject to the liability of that Section. These certifications shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Exchange Act, except to the extent that the Corporation specifically incorporates these certifications by reference in such filing.