Fresh Market 10-Q 2013 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 The Fresh Market, Inc. (the “Company”) on Form 10-Q for the period ended October 27, 2013 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Craig Carlock, President and Chief Executive 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, 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 result of operations of the Company.

/s/ Craig Carlock

Craig Carlock

President and Chief Executive Officer

November 26, 2013

The foregoing certification is being furnished as an exhibit of the Report pursuant to Item 601(b)(32) of Regulation S-K and Section 906 of the Sarbanes-Oxley Act of 2002 and, accordingly, is not being filed with the Securities and Exchange Commission as part of the Report and is not to be incorporated by reference into any filing of the Company under the Securities Act of 1933 or the Securities Act of 1934 (whether made before or after the date of the Report, irrespective of any general incorporation language contained in such filing).