Anderson left Saturday's win over Mercer after a player cut block him. He walked off under his own power but went to the locker room after being looked at by the athletic trainers.
Alabama coach Nick Saban said Anderson will likely not practice on Monday but that his prognosis is positive.
"We feel a little more encouraged than after the game," Saban said. "We'll just see how he progresses throughout the course of the week."
Anderson, a preseason All-SEC selection, ranked third in the SEC in tackles for loss last season.
The top-ranked Crimson Tide are already without another of its starting outside linebackers, Christopher Allen, who suffered a foot injury that Saban said will likely end his season.