Hunt, who was injured the previous week in a loss to Notre Dame at MetLife Stadium in New Jersey, broke his fibula in the fourth quarter of Friday night's game against Louisville in the Carrier Dome.
Syracuse lost 28-6, its third straight, and faces top-ranked Florida State at home on Saturday. Hunt is expected to be out 4-6 weeks.
Shafer also announced a shakeup of his staff. Offensive coordinator George McDonald is being replaced by quarterbacks coach Tim Lester. McDonald will remain on staff in charge of the receivers, Shafer said.