The school announced the surgery Monday, saying Luck hurt the finger in the season finale against Notre Dame on Nov. 28. Luck will miss two to three weeks of practice.
Coach Jim Harbaugh says Luck could be back to play for the 19th-ranked Cardinal (8-4) in the Sun Bowl against Oklahoma on Dec. 31. Harbaugh says senior Tavita Pritchard will probably start the game. Pritchard started 19 games the past two seasons.
Stanford is playing its first bowl game since losing the Seattle Bowl to Georgia Tech in 2001.