Dawson said he suffered the injury when he slammed his hand on a table in frustration while watching a film session Thursday morning.
He is scheduled for surgery Thursday night.
"I'll be fine," Dawson said, according to the Detroit Free Press. "I was out with an ACL injury [freshman] year, and I came back from it."
The 6-foot-6 junior is averaging 10.2 points and 8.7 rebounds this season for the No. 3 Spartans (18-1, 7-0 Big Ten), who have dealt with a bevy of injuries this season.
Starting big man Adreian Payne has missed the past four games with a foot injury and is doubtful to play in Saturday's first-place matchup against Michigan. Leading scorer Gary Harris missed three games earlier this season due to injury, and backup point guard Travis Trice has also missed two games due to injury.