The injury, a torn plantar plate, occurred in UNLV's 27-20 loss to Arkansas State on Saturday. Sanchez didn't want to put an exact time frame on Rogers' expected recovery time but estimated it would take roughly six weeks.
With Rogers unavailable, the Rebels will turn to former Cal quarterback Max Gilliam to start in his place. Gilliam has not attempted a pass at the FBS level. He redshirted at Cal in 2016 before transferring to Saddleback College in Arizona, where he threw for 1,185 yards last season.
Rogers has completed 34 of 82 passes in four games this season for just 369 yards, but is the team's leading rusher (71 carries, 488 yards, 6 TDs).
The Rebels (2-2) have a bye this week before opening Mountain West play against New Mexico on Oct. 6.