WASHINGTON—Special counsel Robert Mueller was authorized in a secret memo to investigate former Trump campaign chairman Paul Manafort’s work for the Ukrainian government, in addition to alleged collusion with Russian officials to interfere in the 2016 elections, according to court filings.

The classified August memo from Deputy Attorney General Rod Rosenstein was disclosed in a court filing by Mr. Mueller’s prosecutors. It seeks to counter arguments by Mr. Manafort’s lawyers that his indictment should be thrown out. Mr. Manafort...