The specifics of the injury were not provided, but Costello is expected to return healthy for training camp. Sports Illustrated previously reported it was a hip injury.
Shaw announced on signing day that the program's only other scholarship quarterback, Davis Mills, would also be out for spring practice due to a knee injury.
Keller Chryst, who began the 2017 season as the starting quarterback, lost his job to Costello midway through the season. Chryst left the program and will pursue a graduate transfer opportunity.
The only other quarterback on the roster is Jack Richardson, a walk-on from Salinas, California, who appeared in one game as a redshirt freshman in 2017 but has not thrown a pass in a game.