AutoZone (AZO) 10-Q 2012 Q3 Quarterly report

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 of AutoZone, Inc. (the “Company”) on Form 10-Q for the period ended May 5, 2012, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William C. Rhodes, III, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

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

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

June 13, 2012

/s/ WILLIAM C. RHODES, III

William C. Rhodes, III

Chairman, President and Chief Executive Officer

(Principal Executive Officer)