Graham went down untouched Sunday after catching a pass from Josh Freeman. Blount fell to the turf before being hit for a 2-yard loss.
He needed help leaving the field, struggling to put weight on his right leg. He was taken to the locker room for an examination and ruled out for the rest of the game.
Graham was starting for Blount for the second straight week. The 31-year-old Graham was coming off his best game in three years, rushing for 109 yards in a win over the New Orleans Saints last week.
He had two carries for 13 yards against the Bears before being hurt.
Kregg Lumpkin took the majority of the snaps after Graham's injury Sunday. He rushed eight times for 15 yards, but also caught six passes for a total of 37 yards.
Information from The Associated Press contributed to this report.