WASHINGTON—A federal judge ruled Wednesday that former Trump campaign chairman Paul Manafort lied to investigators about his contact with an associate the FBI has linked to Russian intelligence despite agreeing to a plea deal requiring him to tell the truth.

U.S. District Judge Amy Berman Jackson said in a four-page order that the government met its burden of proof in showing that Mr. Manafort intentionally misled investigators on at least three matters. Her ruling voids the government’s obligations under the agreement to...