Pursuant to Rule 497(e)

Registration No. 002-85370

SunAmerica Money Market Funds, Inc.

(the “Company”)

SunAmerica Municipal Money Market Fund

(the “Fund”)

Supplement dated January 20, 2012 to the Prospectus dated April 29, 2011, as supplemented and amended to date

On January 17, 2012, the Board of Directors of the Company approved a Plan of Liquidation (the “Plan”) for the SunAmerica Municipal Money Market Fund, a series of the Company, pursuant to which the Fund will be liquidated (the “Liquidation”) on or about March 2, 2012 (the “Liquidation Date”), subject to shareholder approval. If shareholders approve the Plan, the distribution of Liquidation proceeds to shareholders of record as of the close of business on the day prior to the Liquidation Date will occur on the Liquidation Date.

As previously announced in a supplement to the Fund’s prospectus dated December 5, 2011, the Fund closed to new investments on January 13, 2012, and no longer accepts orders to buy Fund shares from new investors or existing shareholders (although reinvestments of any dividends and capital gain distributions from existing shareholders continue to be permitted).

As anticipated, the closing of the Fund to new investments resulted in a significant redemption of Fund shares by shareholders who hold Fund shares through brokerage accounts that utilized the Fund as a cash “sweep” vehicle (“sweep accounts”). Due to the size of the remaining assets in the Fund, the Fund has had to depart from its stated investment strategies and techniques, although the Fund continues to seek to maintain a stable share price of $1.00 and to follow the rules of the Securities and Exchange Commission applicable to money market funds relating to the credit quality, liquidity, diversification and maturity of investments. If the Liquidation is approved by shareholders, the Fund will cease to engage in any investment activities, except for the purpose of winding up its business and affairs, preserving the value of its assets, discharging or making reasonable provision for the payment of all of its liabilities and distributing its remaining assets to shareholders in accordance with the Plan.

The closing of the Fund to new investments (and Liquidation, if approved by shareholders) does not restrict shareholders from selling shares of the Fund and shareholders may redeem their shares at any time (up until the Liquidation Date, if the Liquidation is approved by shareholders), in accordance with the terms set forth in the Fund’s prospectus.

On or about February 23, 2012, the Fund expects to convene a special meeting of shareholders to vote on the Plan. Shareholders of record of the Fund as of the close of business on January 19, 2012 are entitled to notice of and to vote at the special meeting, and will receive proxy materials describing the Liquidation and Plan in greater detail.

Capitalized terms used in this supplement shall, unless otherwise defined herein, have the same meaning as given in the Prospectus.

This Supplement should be retained with your Prospectus for future reference.

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