Exhibit 32

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 Report on Form 10-Q of Family Dollar Stores, Inc. (the “Company”) for the quarterly period ended May 26, 2012, as filed with the Securities and Exchange Commission on the date hereof (the “Form 10-Q”), Howard R. Levine, as Chief Executive Officer of the Company and Mary A. Winston, as Chief Financial Officer of the Company, each certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

• the Form 10-Q fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

• the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: June 29, 2012

/s/ Howard R. Levine

      Howard R. Levine

      Chairman of the Board and Chief Executive Officer

      (Principal Executive Officer)

/s/ Mary A. Winston

      Mary A. Winston

      Executive Vice President – Chief Financial Officer

      (Principal Financial Officer and Principal Accounting Officer)

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.