Peterson sustained the injury in the final minute of the first quarter during Sunday's 27-21 loss to Oakland.
He was helped off the field by trainers and rode a cart into the tunnel where he received an x-ray.
The x-ray came up negative, but an MRI Monday morning showed the sprain.
"He'll probably be in a boot for the next couple of days," Frazier said. "We'll try to see if he's able to do anything on Friday to determine whether he'll be able to play on Sunday or not."
Peterson ran for a score in the first quarter against the Raiders, finishing with 26 yards on six carries.
The five-year veteran out of Oklahoma leads the NFL in rushing touchdowns with 11 and has totaled 872 yards through 10 games.
Gerhart has 118 yards on 24 carries through 10 games this season, while Booker has appeared in four games, carrying the ball four times for 34 yards.