He suffered the injury in Tuesday night's win over Kentucky. Bruner's procedure Wednesday morning was performed by Dr. Lyle Cain of Andrews Sports Medicine in Birmingham.
Alabama said there was no specific timetable for Bruner's return but he is expected to make a full recovery and play again this season.
Bruner is averaging 7.8 points and 5.9 rebounds. The 6-foot-10, 225-pound graduate transfer from Yale leads the team in blocks (16) and steals (20).
The Crimson Tide has won its first five Southeastern Conference games and six in a row overall.