Burke, a preseason first-team All-American, led Michigan with 14.8 points and 4.6 assists last season.
"Trey's a good kid," Michigan coach John Beilein said Wednesday. "We talked about he's going to sit out this game and he's going to learn a very valuable experience."
Beilein decided to suspend Burke after making what Beilein called "some out-of-character decisions he now regrets." Beilein declined to further comment on the suspension.
Freshman point guard Spike Albrecht will start in place of Burke.
Beilein also said redshirt sophomore forward Jon Horford will not play Thursday as he continues to recover from a knee strain suffered last week in practice. Freshman Mitch McGary, however, will play as he recovers from a foot injury.