WASHINGTON—Two donors to a pro-Trump fundraising committee who helped Rudy Giuliani’s efforts to investigate Democrat Joe Biden were arrested late Wednesday on criminal charges stemming from their alleged efforts to funnel foreign money into U.S. elections and influence U.S. politics on behalf of at least one unnamed Ukrainian politician.

In an indictment unsealed Thursday, federal prosecutors in Manhattan alleged Lev Parnas and Igor Fruman were engaged in political activities in the U.S. on behalf of one or more Ukrainian...