<Page>

                                                             Exhibit 99.906.Cert

                Certification Pursuant to 18 U.S.C. Section 1350,
                             As Adopted Pursuant to
                  Section 906 of the Sarbanes-Oxley Act of 2002

Name of Issuer: Morgan Stanley Institutional Fund, Inc.

     In connection with the Report on Form N-CSR (the "Report") of the
above-named issuer for the period ended December 31, 2004 that is accompanied by
this certification, the undersigned hereby certifies 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 Issuer.


Date: February 17, 2005                  /s/ Ronald E. Robison
                                         -----------------------------
                                         Ronald E. Robison
                                         Principal Executive Officer


A signed original of this written statement required by Section 906 has been
provided to Morgan Stanley Institutional Fund, Inc. and will be retained by
Morgan Stanley Institutional Fund, Inc. and furnished to the Securities and
Exchange Commission or its staff upon request. This written statement required
by Section 906 is being furnished with this report, but not being filed as part
of this Report.

<Page>

                Certification Pursuant to 18 U.S.C. Section 1350,
                             As Adopted Pursuant to
                  Section 906 of the Sarbanes-Oxley Act of 2002

Name of Issuer: Morgan Stanley Institutional Fund, Inc.

     In connection with the Report on Form N-CSR (the "Report") of the
above-named issuer for the period ended December 31, 2004 that is accompanied by
this certification, the undersigned hereby certifies 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 Issuer.


Date: February 17, 2005                  /s/ James Garrett
                                         --------------------------------
                                         James Garrett
                                         Principal Financial Officer


A signed original of this written statement required by Section 906 has been
provided to Morgan Stanley Institutional Fund, Inc. and will be retained by
Morgan Stanley Institutional Fund, Inc. and furnished to the Securities and
Exchange Commission or its staff upon request. This written statement required
by Section 906 is being furnished with this report, but not being filed as part
of this Report.