For years, a river of American wealth has flowed into Russia — money from virtually every corner of the U.S. financial world. Public pensions, hedge funds, banks, insurers, university endowments, mutual funds and wealthy investors have collectively showered billions of dollars on Vladimir Putin’s regime and supported companies closely connected to it.

Teachers, firefighters, police officers and state employees from New York to California might be surprised to learn that their retirement dollars are invested in shares of sanctioned Russian companies.

The nation’s two biggest public pension funds...