U.S. investigators are looking into Malaysian Prime Minister Najib Razak’s assets as part of a series of global probes linked to a troubled state investment fund, according to people familiar with the matter.

The U.S. Justice Department’s Kleptocracy Asset Recovery Initiative has been investigating the case, which involves people and entities connected to the state-run fund 1Malaysia Development Bhd., the people said. The Federal Bureau of Investigation also is involved with the inquiries, The Wall Street Journal reported...