Anderson sustained the injury during the second quarter of the Sooners' 49-21 win over UCLA on Saturday.
"We're heartbroken for him," Oklahoma head coach Lincoln Riley said. "He's overcome so much in his career, and if anybody can do it again it's Rodney.
"He's played a lot of great football and has a lot more ahead of him. He's just a tremendous person and player and we'll miss him on the field. But we know he'll be with us every step of the way as a team captain, and that other players will step up in his place."
The redshirt junior was named to the preseason All-Big 12 first-team after an electrifying 2017.
Anderson rushed for 19 yards and a touchdown on six carries against the Bruins before the injury. He posted 1,161 yards with 13 scores on the ground last year.