Lindholm, a first-round pick (No. 5) by the Carolina Hurricanes in the 2013 NHL Draft, finished his rookie season with 21 points (nine goals, 21 points) in 58 games. He bumped those numbers up to 39 points (17 goals, 22 assists) in 2014-15.

After a 16-goal, 44-point season in 2017-18, the Hurricanes traded Lindholm to the Calgary Flames with defenseman Noah Hanifin on June 23, 2018, for defenseman Dougie Hamilton, forward Micheal Ferland and defenseman prospect Adam Fox.

Lindholm was traded to the Vancouver Canucks by the Flames on Jan. 31, 2024. He scored two power-play goals in his first game with the Canucks, a 3-2 win at the Carolina Hurricanes on Feb. 6. That made him the fifth player in team history to score multiple times in his debut, joining Greg Adams (four on Oct. 8, 1987), Esa Tikkanen (two on Jan. 3, 1996), Thomas Gradin (two on Oct. 11, 1978) and Claire Alexander (two on Jan. 28, 1978).

Lindholm signed a seven-year contract with the Boston Bruins on July 1, 2024. He was named to Sweden's roster for the 4 Nations Face-Off during the 2024-25 season.

Lindholm's father, Mikael, was a veteran in the Swedish Elite League who also played 18 games with the Los Angeles Kings during the 1989-90 season. His cousin Calle Jarnkrok plays for the Nashville Predators, and his brother Oliver plays in the Swedish third division.

Internationally, Lindholm helped Sweden win silver medals at the 2012 World Under-18 Championship and the 2013 World Junior Championship, as well as a gold medal at the 2017 IIHF World Championship.