Kapanen was selected by the Pittsburgh Penguins in the first round (No. 22) in the 2014 NHL Draft after he had 14 points (seven goals, seven assists) in 47 games with KalPa of Liiga, Finland's top pro league.

Kapanen's father, Sami Kapanen, had 458 points (189 goals, 269 assists) in 831 games during 12 NHL seasons and played in the Stanley Cup Final with the Carolina Hurricanes in 2002.

On July 11, 2014, Kasperi Kapanen signed a three-year, entry-level contract with the Penguins.

Kapanen played for KalPa in 2014-15 and had 21 points (11 goals, 10 assists) in 41 games before playing four games with Wilkes-Barre of the American Hockey League.

On July 1, 2015, Kapanen was acquired by the Toronto Maple Leafs in the trade that sent forward Phil Kessel to the Penguins. He played for Finland at the 2016 IIHF World Junior Championship and had five points (two goals, three assists) in seven games. He scored the game-winning goal 1:33 into overtime against Russia to give Finland the gold medal.

He played in 44 games and had 25 points (nine goals, 16 assists) for Toronto of the AHL in 2015-16 and was called up by the Maple Leafs on Feb. 29, 2016. Kapanen made his NHL debut that night against the Tampa Bay Lightning.

The following season, Kapanen had 43 points (18 goals, 25 assists) in 43 games for Toronto of the AHL and appeared in eight games for the Maple Leafs, scoring his first NHL goal in a 5-3 win against the Penguins on April 8, 2017. In Game 2 of the Eastern Conference First Round against the Washington Capitals, Kapanen scored the game-winning goal at 11:53 of the second overtime. He had two goals before the Maple Leafs were eliminated from the Stanley Cup Playoffs in six games.

Kapanen played 38 games in 2017-18 and had nine points (seven goals, two assists), as well as one goal in seven Stanley Cup Playoff games. After the season, he played for Finland at the 2018 IIHF World Championship and scored three goals in eight games.

When forward William Nylander remained unsigned for the first two months of the 2018-19 season, Kapanen used the opportunity to claim a regular spot with the Maple Leafs, scoring 20 goals and finishing with 44 points in 78 games. He followed that with 13 goals and 36 points in 69 games in 2019-20.

Kapanen signed a two-year, $6.4 million contract with the Penguins on July 21, 2022 as a restricted free agent and avoided a salary arbitration hearing. He was claimed off waivers by the St. Louis Blues on Feb. 23, 2023, and signed a one-year, one-million contract with the Blues on July 1, 2024. He had 22 points (six goals, 16 assists) in 73 games of his first full season in St. Louis.

Kapanen signed a one-year, $1 million contract to stay with the Blues on July 1, 2024. He was claimed off waivers by the Edmonton Oilers from the St. Louis Blues on Nov. 19, had 13 points (five goals, eight assists) in 57 games and scored at 7:19 of overtime to give the Oilers a 1-0 win against the Vegas Golden Knights in Game 5 of the second round that sent them to the Western Conference Final for the second consecutive season and third in four years.

Kapanen signed a one-year, $1.3 million contract to stay with the Oilers on June 30, 2025, in lieu of becoming an unrestricted free agent.