During the 2008–09 season, Callahan was a member of the Kelowna Rockets team that won the Ed Chynoweth Cup, in his debut season with the club. During the 2010–11 season, Callahan helped Kelowna to a B.C. Division title, by finishing second among team leaders with 23 goals, and third among team leaders with 31 assists. Callahan was named the WHL player of the week for the week ending November 6, 2010, after recording five goals and seven assists in four games. During Callahan's three seasons with the Kelowna Rockets, he registered 57 goals, 128 points, and 440 penalty minutes in 204 games played.
On May 4, 2010, the Detroit Red Wings signed Callahan to a three-year entry-level contract.
Callahan made his AHL debut with the Grand Rapids Griffins on October 8, 2011. During his first professional season, which was limited to 48 games due to injuries, Callahan finished second among AHL rookies with 14 fighting majors.
During the 2012–13 season, Callahan skated in 71 of 76 games in his second season in the AHL. On January 19, 2013, Callahan recorded his first professional hat-trick in a game against the Rockford IceHogs. Callahan tied for the team lead in the Calder Cup Finals with five points, helping lead the Griffins to the Calder Cup.
On March 25, 2014, Callahan made his NHL debut for the Detroit Red Wings in a game against the Columbus Blue Jackets.
During the 2013–14 season, Callahan skated in 70 games in his third season in the AHL, and finished among the Griffins' leading scorers with 26 goals (2nd) and 44 points (4th).
On July 17, 2014, the Detroit Red Wings signed Callahan to a one-year contract.
During the 2014–15 season, Callahan recorded 16 goals and 22 assists in 48 games during his fourth season in the AHL, before a knee injury sidelined him for the remainder of the season.
On July 13, 2015, the Detroit Red Wings signed Callahan to a one-year contract extension.
On July 21, 2016, the Detroit Red Wings signed Callahan to a one-year contract extension. On March 1, 2017, Callahan was recalled by the Red Wings. Prior to being recalled, he recorded 14 goals and 22 assists in 53 games for the Griffins. On March 20, Callahan was returned to the Griffins. During the 2016–17 season, Callahan recorded 16 goals and 27 assists in 66 regular season games for the Griffins. During the 2017 Calder Cup playoffs he recorded six goals and 10 assists in 19 playoff games, to help lead the Griffins to the Calder Cup.
On July 1, 2017, Callahan left the Red Wings and signed as a free agent to a two-year, two-way contract with the Edmonton Oilers.
Callahan represented the United States at the 2011 World Junior Ice Hockey Championships, where he won a bronze medal. Callahan's only goal in the tournament was a game-winning goal against Switzerland in the final preliminary-round game to give the team a bye into the medal round.