The Bears (1-3) have not issued an official statement, but the Chicago Tribune said it is likely that Jones will miss this Sunday's game against Minnesota.
Jones is also expected to visit notable sports surgeon Dr. James Andrews for a second opinion.
"Cedric is next in the rotation, but I was pleased with what Adrian Peterson did," head coach Lovie Smith told the paper. "He's a good running back."
Jones has rushed for three straight 100-yard games this season and has 413 rushing yards on the year with four touchdowns. Jones has also caught 11 passes for 41 yards.
In limited action, the highly touted Benson has ran for 65 yards on 24 carries and no touchdowns.