Johnson was accused of the sexual assault in March, the month after it allegedly occurred, The Missoulian reported.
After formal charges were filed, Johnson was immediately suspended from the Grizzlies football team, the newspaper said.
Charging documents allege Johnson and the woman were watching a movie in her bedroom in Missoula on Feb. 4 when he began kissing her. The woman said she kissed him back, but said she just wanted to watch the movie. He persisted despite her repeated "no's," until the sex act occurred, the documents allege.
Johnson has maintained his innocence, saying the sex was consensual.
The charge against Johnson is the latest controversy to envelop UM. In February, a running back for the football team was charged with sexual intercourse without consent. The dean of students resigned this year after it was revealed he had informed a Saudi exchange student he had been accused of rape. The student left the country, but the school did not notify the police.
The NCAA is also investigating the football team over unspecified allegations, the newspaper said.