The fourth-year back last played in a 24-17 loss to the Raiders on October 16, and has 60 carries for 211 yards and two touchdowns this season.
"We want him to get healthy," Cleveland head coach Pat Shurmur said. "Peyton's out this week and he's going to be rehabbing his hamstring."
Shurmur also said that Montario Hardesty will "most likely be out" for Sunday's game.
The Tennessee product has 244 yards rushing on 75 carries, and 12 receptions for 113 yards in seven games played this year.
If Hardesty can't go, Chris Ogbonnaya will most likely make his second consecutive start.
"We're going to look every way we can to improve our roster," Shurmur said when asked if the Browns are looking to bring in another running back.
Ogbonnaya carried the ball 13 times for 28 yards in Sunday's 30-12 loss to Houston, and the Browns mustered just 44 yards total on the ground.