SUPPLEMENT DATED JUNE 12, 2020 TO THE PROSPECTUS OF

Morgan Stanley California Tax-Free Daily Income Trust, dated April 30, 2020
Morgan Stanley New York Municipal Money Market Trust, dated April 30, 2020
Morgan Stanley Tax-Free Daily Income Trust, dated April 30, 2020
Morgan Stanley U.S. Government Money Market Trust, dated May 29, 2020

Effective July 1, 2020, the third sentence in the section of each Prospectus entitled "Shareholder Information—How to Exchange Shares—Permissible Fund Exchanges" is hereby deleted and replaced with the following:

Because purchases of Class A shares of Morgan Stanley Institutional Fund Trust Liquid Assets Prime, Ultra-Short Income and Ultra-Short Municipal Income Portfolios are not subject to a sales charge, and purchases of Class A shares of Morgan Stanley Institutional Fund Trust Short Duration Income Portfolio are subject to a reduced sales charge, you may be subject to the payment of a sales charge by your Financial Intermediary, at time of exchange into Class A shares of a Morgan Stanley Fund, based on the amount that you would have owed if you directly purchased Class A shares of that Morgan Stanley Fund (less any sales charge previously paid in connection with shares exchanged for such shares of Morgan Stanley Institutional Fund Trust Liquid Assets Prime, Short Duration Income, Ultra-Short Income or Ultra-Short Municipal Income Portfolios, as applicable).

PLEASE RETAIN THIS SUPPLEMENT FOR FUTURE REFERENCE.