A Russian metals billionaire sued President Donald Trump’s former campaign chairman on Wednesday, alleging he and a partner misappropriated at least $18.9 million of funds the Russian had invested.

Oleg Deripaska alleged in a lawsuit filed in the New York state court Wednesday that Paul Manafort, the former campaign manager, and his long-time partner Richard Gates “vanished” the money invested by the Russian businessman in the late 2000s. The suit, filed by Mr. Deripaska’s Cyprus-based Surf Horizon Ltd., seeks $25 million...