The precise timetable for recovery is unclear, but a source said it is unlikely that Webb will participate in spring practice. With freshman Pat Mahomes playing baseball, that could open the team's quarterback competition for highly regarded signee Jarrett Stidham.
Stidham, an Elite 11 participant this past summer, intends to enroll in January.
Mahomes started for Texas Tech after Webb suffered an ankle injury Oct. 25 at TCU. He set a Big 12 freshman record with his 593 yards on 30 of 56 passing that included six touchdowns, in the team's 48-46 loss to Baylor on Saturday.
Walk-on Vincent Testaverde Jr., the son of the former Heisman Trophy winner by the same name, also played this season for the Red Raiders.
Texas Tech has played four freshman quarterbacks, including two walk-ons, the past two seasons.
Webb initially suffered the shoulder injury Sept. 25, when he landed awkwardly on his left side late in the team's loss at Oklahoma State. He was cleared to play the following week, but Webb and the team's coaching staff have known since then that he would eventually need surgery.
Webb threw for 2,539 yards and 24 touchdowns in eight games, but he also had a disconcerting number of turnovers. Seven of Webb's 13 interceptions came after the arm injury.
Information from the Associated Press was used in this report.