Butt enrolled at the University of Michigan in 2013. As a freshman, he appeared in 13 games, eight as a starter for the 2013 Michigan Wolverines football team. His playing time increased after Devin Funchess moved from tight end to wide receiver.Butt caught 20 passes for 235 yards and two touchdowns and was selected by ESPN.com as a member of the All-Big Ten Conference freshman team.As a sophomore, he missed the first two games while recuperating from a torn ACL. He appeared in 10 games in 2014, five as a starter, and recorded 21 passes for 211 yards and two touchdowns. As a junior in 2015, Butt had a career-high eight receptions for 95 yards in the season opener against Utah. His eight catches was the most by a Michigan tight end since 1995.After the game, head coach Jim Harbaugh said of Butt: "He's a football player. I can't give a better compliment.During the 2015 season, Butt had 51 catches for 654 yards (12.8 yds/catch) and three touchdowns. Following the 2015 season, Butt was named the Kwalick–Clark Tight End of the Year, named to the All-Big Ten offensive first-team, by both the coaches and media, and named a First-Team All-American.