Certification Pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of
the Sarbanes-Oxley Act of 2002; provided by the Chief Executive Officer and
Chief Financial Officer, based on each such officer's knowledge and belief.

The undersigned officers of Nuveen Massachusetts Premium Income Municipal Fund
(the "Fund"), certify that, to the best of each such officer's knowledge and
belief:

     1.   The Form N-CSR of the Fund for the period ended November 30, 2008
          (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 Fund.

Date: February 6, 2009
      -----------------------

                                           /s/ Gifford R. Zimmerman
                                               ---------------------------------
                                               Gifford R. Zimmerman
                                               Chief Administrative Officer
                                               (principal executive officer)

                                           /s/ Stephen D. Foy
                                               ---------------------------------
                                               Stephen D. Foy
                                               Vice President, Controller
                                               (principal financial officer)