Litton, a sophomore, suffered a concussion in last week's loss to Akron and was not cleared by the school's medical staff, a source said.
Freshman Garet Morrell is expected to make his first start against the No. 3-ranked Cardinals. He has completed 2 of 8 pass attempts this season.
The 6-foot-6 Litton threw for 722 yards and 10 touchdowns in the Thundering Herd's first two games.
Last season, Litton won the starting job after the Herd's third game and led Marshall to a 10-3 record and a win against UConn in the St. Pete Bowl. He finished his freshman season with 2,605 yards passing, 23 TDs and 8 interceptions.