The injury, which will require surgery, occurred late in the 78-74 win against Boise State on Friday in a game he scored a career-high 25 points.
In four games this season, the Canton, Miss., native was averaging a team-high 18.8 rebounds and led MSU with nine dunks.
"I can't even begin to tell you how bad I feel for Q," MSU coach Ben Howland said. "He's worked so hard to get where he's at, but he knows he has the support of everyone on this team, and I expect him to fully recover and be back with us full strength next year."
The Bulldogs, 3-1 on the year, posted a 2-1 mark in Charleston, S.C., this past week and will return to action at 7 p.m. on Friday at Humphrey Coliseum against Lehigh.