He is scheduled to undergo an MRI on Monday.
He suffered the injury at the end of the first half of Sunday’s 27-23 win over the Detroit Lions.
While trying to run for a first down, Orton was tackled by Cory Redding then appeared to get his ankle banged by end Dewayne White, who cleaned up on the play. Orton attempted to stand up but fell back to the ground.
He was carted off the field with 26 seconds left before halftime.
Being out a month could keep Orton from facing some good teams including Tennessee, Green Bay, St. Louis and Minnesota.
Rex Grossman replaced Orton against the Lions and scored the game-winning, 1-yard touchdown.
Orton had started the first eight games and was one of the hottest quarterbacks in the league before the injury.
He won the starting job in training camp over Grossman.