Investors who thought they steered clear of Facebook Inc.'s initial public offering should take a closer look at their mutual funds.

At least 160 U.S.-based mutual funds and exchange-traded funds, including those run by Fidelity Investments, Morgan Stanley Investment Management Inc. and OppenheimerFunds Inc., bought shares of Facebook in May, according to monthly disclosures made in June and July compiled by investment-research firm Morningstar Inc. for The Wall Street Journal.

Some...