RIO DE JANEIRO—A Brazilian judge authorized an investigation into whether U.S. Olympic gold medalist Ryan Lochte and teammate Jimmy Feigen broke the law by giving a false account of a crime, citing contradictions in their testimony over an alleged armed robbery.

In a court order dated Wednesday and seen by The Wall Street Journal, Judge Keyla Blanc De Cnop also banned Messrs. Lochte and Feigen from leaving Brazil. However, Mr. Lochte’s father said in a text message Wednesday that his son was already “back in the U.S.,” and...