<Page>

                                                                    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 FedEx Corporation ("FedEx") on Form 10-K
for the period ended May 31, 2004 as filed with the Securities and Exchange
Commission on the date hereof (the "Report"), I, Frederick W. Smith, Chairman,
President and Chief Executive Officer of FedEx, 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 results of operations
          of FedEx.


Date:  July 16, 2004


/s/ Frederick W. Smith
- -----------------------
Frederick W. Smith
Chairman, President and
Chief Executive Officer