Glasgow told the court he had consumed alcohol after he blew a .086 on a Breathalyzer test Sunday morning.
Glasgow was arrested on drunken-driving charges last April. He pleaded guilty in June to driving while visibly impaired and received a sentence that included taking alcohol-education classes and submitting to random tests for drugs and alcohol.
Glasgow's positive test Sunday was a violation of his probation.
Michigan coach Jim Harbaugh released a statement Monday that said Glasgow was suspended from the team.
"We have been made aware of Graham's probation violation and he has been suspended," Harbaugh said. "Graham will be subject to punishment through the judicial system, the student-athlete alcohol policy and the Michigan football program."
Glasgow started 24 games during the two previous seasons, splitting his time between guard and center. Michigan's starting center from the 2014 season, would-be redshirt senior Jack Miller, announced last week he no longer wanted to play football.
Glasgow took over Miller's vacant spot in the middle of the offensive line last week during practice, according to his teammates.