WASHINGTON—Special Counsel Robert Mueller is investigating possible money laundering by Paul Manafort, Donald Trump’s former campaign manager, as part of his criminal investigation into what U.S. intelligence agencies say was a Kremlin-backed campaign to meddle in the 2016 presidential election, according to a person familiar with the matter.

The inquiry into the issue by Mr. Mueller, a former director of the Federal Bureau of Investigation, and his team began several weeks ago, this person said. A spokesman for Mr. Manafort,...