SECTION 906 CERTIFICATION

Certification Pursuant to 18 U.S.C. Section 1350,

As Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

Morgan Stanley U.S. Government Money Market Trust

In connection with the Report on Form N-CSR (the “Report”) of the above-named issuer for the period ended January 31, 2020 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: March 17, 2020	/s/ John H. Gernon
	John H. Gernon
	Principal Executive Officer

SECTION 906 CERTIFICATION

Certification Pursuant to 18 U.S.C. Section 1350,

As Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

Morgan Stanley U.S. Government Money Market Trust

In connection with the Report on Form N-CSR (the “Report”) of the above-named issuer for the period ended January 31, 2020 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: March 17, 2020	/s/ Francis Smith
	Francis Smith
	Principal Financial Officer