Washington was hurt in Saturday night's home overtime victory against Eastern Michigan. The Aztecs (3-1) are off Saturday before opening Mountain West Conference play at Boise State on Oct. 6.
Washington has 560 yards and five touchdowns on 99 carries. The Aztecs were hoping he'd follow D.J. Pumphrey and Rashaad Penny as a 2,000-yard rusher.
His replacement, sophomore Chase Jasmin, has 244 yards and one score on 43 carries.
Washington also sat out most of the fourth quarter of a home win against Arizona State on Sept. 15. He said he was "banged up a little bit" after carrying 27 times for 138 yards and a score.