That depends on which money market fund you have invested in. There are big differences between a money market mutual fund and a money market deposit account at a bank. Some banks sell both types of investments.
Money market mutual funds invest in what was thought to be highly liquid safe securities. Safe, that is, until this past week. Money market mutual funds make investments in asset backed commercial paper, certificates of deposits and government securities. One money market mutual fund, The Primary Fund, froze redemptions for seven days because the fund “broke the buck”, which means each share in the fund is worth less then $1.00, in this case each share is now worth 97 cents. The Primary Fund got into trouble because of its exposure to Lehman Brothers (Lehman filed for bankruptcy this week), the fund invested in Lehman debt.
Money market deposit accounts are FDIC insured up to $100,000 per account, $200,000 for joint accounts and up to $250,000 for some retirement accounts.
Be sure to check with your financial institution to see which type of money market account you have money invested in.
Update: 9/19/08 Treasury Department to guarantee Money market mutual funds
The Treasury said it will tap into a Depression-era fund to provide guarantees for the money market mutual funds. The Treasury also said it would use its $50 billion from the Exchange Stabilization Fund to provide the guarantees for the money market mutual funds. The fund was created in 1934 to provide support for the dollar.