A native of Chesterton, Indiana, McGary declared for the NBA draft after completing his sophomore season for the 2013–14 Michigan Wolverines men's basketball team.

He eventually transferred to Brewster Academy, a prep school in Wolfeboro, New Hampshire, to repeat his junior year because his parents thought the discipline would be good for him.

[24] In a press conference broadcast on ESPNU on November 3, 2011, McGary announced his verbal commitment to Michigan over his other two finalist Florida and Duke.

[32] Brewster entered the 2012 NEPSAC Class AAA Boys' Basketball Tournament undefeated and ranked number 1 in the nation according to the Five-Star Basketball Rankings published in Sports Illustrated,[33] but lost in the semifinals of the tournament to Northfield Mount Hermon School, who was led by future teammate Spike Albrecht, in overtime on March 2.

[41][42] JaKarr Sampson earned both the 2012 National Prep Championship MVP and New England Preparatory School Athletic Council (NEPSAC) AAA Player of the Year,[39][43] leaving McGary with a supporting role.

Sources: The 2011–12 Michigan Wolverines men's basketball team had been co-champions of 2011–12 Big Ten Conference,[48] but lost both of its co-captains, Zack Novak and Stu Douglass, to graduation and three players as transfers.

[49][50] The team was returning a nucleus of All-Big Ten players Trey Burke and Tim Hardaway Jr.[51] In the third game of the season and the third of his career, McGary posted a game-high 9 rebounds in 17 minutes of play off the bench against Cleveland State on November 13.

[64] McGary played a career-high 29 minutes, tallying then career highs of 14 points and 4 steals, along with 6 rebounds, on February 5 in an overtime victory against Ohio State.

[72] As a number four seed, Michigan defeated its first NCAA tournament opponent, South Dakota State, 71–56 on March 21 with McGary making his third start of the season and contributing 13 points and 9 rebounds.

[73] The 27th victory of the season gave the team its most wins in 20 years and matched head coach John Beilein's career high.

[81] McGary joined Blake Griffin (2009) as the only two players in the last 15 NCAA Division I men's basketball tournaments to achieve 14 or more rebounds and 21 or more points in back-to-back games.

[82] With his tournament run, McGary became the Big Ten Conference leader in field goal percentage (although he slipped just below Victor Oladipo at the end of the season).

[85] 5 steals tied Ricky Green (1977) and Tom Stanton (1977) as the best single-NCAA Tournament game performance in school history, but was surpassed by Derrick Walton in 2018.

[88][89] Two nights later, Michigan lost in the championship game to Louisville by an 82–76 margin as McGary contributed 6 points, 6 rebounds, a steal, a block and an assist.

[92] McGary finished the season as the Big Ten conference freshman leader in rebounding and placed second to Victor Oladipo in field goal percentage (59.87% vs.

[93] Prior to the Final Four, McGary stated that he would not enter the 2013 NBA draft,[94] but a few days later said he had been caught off guard and would prefer to respond after he has time to reflect on his season.

[95] On April 9 before boarding the airplane to return from the NCAA Final Four, Beilein met with Burke, Hardaway, Robinson and McGary to direct them to seek the advice of the NBA advisory committee.

[96] On April 12, ESPN journalist Myron Medcalf described McGary's likelihood of entering the draft as "borderline," noting that his NCAA tournament performance may have given him a sudden chance to be a lottery selection.

[109] Later that month, McGary joined McDermott, Smart, Wiggins and Julius Randle as first team preseason All-Americans by USA Today Sports 2013-14 College Basketball Preview Magazine.

[116] Dick Vitale selected McGary to his All-Solid Gold preseason first team (along with McDermott, Smart, Russ Smith and Aaron Craft).

[117] On November 4, McGary was named first team preseason All-American by the Associated Press along with Mcdermott, Smart, Wiggins and Smith.

[129] After missing the preseason and first two regular season games, McGary returned to play against Iowa State on November 17 posting 9 points, 6 rebounds and 4 steals.

[130][131][132] McGary posted a 14-point and 12 rebound double-double in his third game, which was the November 22 Puerto Rico Tip-Off semifinal against Florida State.

[133] With leading scorer Stauskas sidelined with an injury, the November 29 contest against Coppin State was McGary's first start of the season.

[143] The 2013–14 team advanced to the elite eight round of the 2014 NCAA Division I men's basketball tournament before being eliminated by Kentucky on March 30.

[151] McGary was tested 18 days before the NCAA decided to reduce the automatic punishment for marijuana use to a half a season and his appeal for lenience was unsuccessful.

[160][161] On October 8 during training camp, McGary fractured the second metatarsal of his left foot, causing him to be sidelined for an estimated six weeks.

[173] On March 13, McGary made his first start against the Minnesota Timberwolves in place of an injured Serge Ibaka,[174] scoring 12 points in 22 minutes.

[176][177] In the April 15 season finale against the Minnesota Timberwolves, McGary posted a season-high 4 blocked shots in just 14 minutes of play.

[180][181] On October 16, 2015, McGary suffered a loose ball collision with Matt Barnes of the Memphis Grizzlies that resulted in concussion-like symptoms.