WASHINGTON—The House Intelligence Committee referred Erik Prince, an informal adviser to President Trump, for criminal prosecution on allegations that he misled the panel, marking the latest fallout from special counsel Robert Mueller’s probe.

Committee Chairman Rep. Adam Schiff (D., Calif.) asked the Justice Department to evaluate whether Mr. Prince lied to Congress in 2017 when he described a meeting in the Seychelles with an associate of Russian President Vladimir Putin. The congressional testimony by Mr. Prince, the billionaire...