The 6-foot, 225-pound sophomore rushed for 223 yards and a touchdown this season while averaging seven yards per carry. He had emerged as the primary backup for starter LaDarius Perkins.
It's the second serious knee injury for Griffin, who tore the ACL in his left knee less than two years ago.
Mississippi State says Griffin suffered the injury during a practice on Saturday and tests revealed the damage. He is scheduled to have surgery on Thursday.
Mississippi State (8-4) faces Northwestern (9-3) in the Gator Bowl on Jan. 1.