Fresh Market 10-K 2010 FY Annual 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 Annual Report of The Fresh Market, Inc. (the “Company”) on Form 10-K for the period ending December 31, 2010 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, Craig Carlock, Chief Executive Officer of the Company, and Lisa Klinger, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to our knowledge, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; 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/    CRAIG CARLOCK        

Craig Carlock

Chief Executive Officer

March 22, 2011