EX-99.906CERT

Section 906 Certifications


                CERTIFICATION PURSUANT TO 18 U.S.C SECTION 1350,

                             AS ADOPTED PURSUANT TO

                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



         JOHN V. MURPHY,  Chief Executive  Officer,  and BRIAN W. WIXTED,  Chief
Financial  Officer,  of Oppenheimer Money Market Fund, Inc. (the  "Registrant"),
each certify to the best of his or her knowledge that:

         1. The Registrant's  periodic report on Form N-CSR for the period ended
July 31, 2004 (the "Form N-CSR") fully complies with the requirements of Section
15(d) of the Securities Exchange Act of 1934, as amended; and

         2. The information  contained in the Form N-CSR fairly presents, in all
material  respects,  the  financial  condition  and results of operations of the
Registrant.  This  certification  is being  furnished to the  Commission  solely
pursuant to 18 U.S.C.  ss. 1350 and is not being filed as part of the Form N-CSR
filed with the Commission.



Chief Executive Officer                     Chief Financial Officer

Oppenheimer Money Market Fund, Inc.         Oppenheimer Money Market Fund, Inc.

/s/John V. Murphy                           /s/Brian W. Wixted
- ----------------------------                ----------------------------
John V. Murphy                              Brian W. Wixted

Date: 9/16/04                               Date:  9/16/04