McCarron was selected by the Montreal Canadiens in the first round (No. 25) of the 2013 NHL Draft. He signed a three-year, entry-level contract July 11, 2013. He played for USA Hockey's National Team Development Program for two seasons (2011-12, 2012-13) and had five points (three goals, two assists) to help the United States win a silver medal at the 2013 IIHF U18 World Championship, losing 3-2 in the final to Connor McDavid and Canada. He also had a goal and an assist with 15 shots on goal at the 2025 IIHF World Championship to help the U.S. win gold for the first time since 1933.

On Jan. 1, 2015, McCarron was acquired by Oshawa of the Ontario Hockey League in a trade with London. He had 27 points (six goals, 21 assists) in 31 games to help Oshawa win the OHL title and the Memorial Cup while being named to the Memorial Cup All-Star Team. He had 38 points (17 goals, 31 assists) in 58 games for St. John's of the American Hockey League in 2015-16 and was selected for the AHL All-Star Classic. He was called up to the Canadiens and made his NHL debut in a 6-2 loss to the Dallas Stars on Dec. 19, 2015 and scored his first goal in a 4-1 loss to the Calgary Flames on March 20, 2016. McCarron finished the season with two points (one goal, one assist) in 20 games. He split the 2016-17 season with St. John's and Montreal. He had 19 points (seven goals, 12 assists) in 32 AHL games and five points (one goal, four assists) with the Canadiens. In 2017-18, He had one assist in 18 games with Montreal and played most of the season with Laval of the AHL, where he had 24 points (seven goals, 17 assists) in 54 games.

The Canadiens traded McCarron to the Nashville Predators for Laurent Dauphin on Jan. 7, 2020. He signed a one-year, $775,000 contract with the Predators on April 16, 2023, coming off the best statistical season of his NHL tenure in 2021-22, when he set career highs in games played (51), goals (seven), assists (seven) and points (14) while winning 54.4 percent of his face-offs. The Predators then gave him a two-year, $1.8 million contact on Feb. 16, 2024.

McCarron was traded to the Minnesota Wild by the Predators on March 3, 2026, for a second-round pick in the 2028 NHL Draft. He led the Predators in hits (165), was third in blocked shots (six), sixth in takeaways (17), and first among their forwards in short-handed ice time per game (2:29) at the time of the deal.