Spartans coach Mark Dantonio said Maxwell sustained the injury falling backward while trying to avoid the rush. Maxwell, projected to be Michigan State's starter in the fall, hasn't been ruled out for the team's spring game on April 28.
Freshman Connor Cook, the only other scholarship quarterback on the roster, will take the majority of reps in practice this week and could play for both sides in the spring game. Maxwell will be re-evaluated early next week, Dantonio said.
"He may (or) may not be back by the end of the spring ball here," Dantonio told reporters before Tuesday's practice. "We'll see how it goes early in the week, next week."
Maxwell, who backed up Kirk Cousins the past two seasons, appeared in four games in 2011 and completed 18 of 26 passes for 171 yards and a touchdown. He had drawn praise for his play this spring before the injury.