Kotkaniemi began his youth career playing with hometown club, Porin Ässät, as a 14-year old at the under-16 level in 2014. Having progressed through the junior ranks and showing offensive potential, Kotkaniemi made his Liiga debut with Ässät to start the 2017–18 season, on 9 September 2017 where he scored his first professional goal. As a 17-year old rookie, Kotkaniemi posted impressive offensive totals, collecting 10 goals and 29 points in 57 games.
Montreal Canadiens
On 22 June 2018, having been touted amongst the top players by the NHL Central Scouting service, Kotkaniemi was drafted third overall in the 2018 NHL Entry Draft by the Montreal Canadiens. After attending the club's development camp, he was signed to a three-year, entry-level contract on 2 July 2018. On 3 October 2018, Kotkaniemi made his NHL debut against the Toronto Maple Leafs; he earned one assist in the loss. He thus became the first person born in the year 2000 to play in one of the Big Four professional sports leagues in North America. Kotkaniemi scored his first NHL goal on 1 November 2018 against the Washington Capitals. At 18 years, 118 days old, he became the second youngest goal scorer in Canadiens' history behind Mario Tremblay, who tallied his first goal at age 18 years, 75 days on 16 November 1974 against the New York Rangers at the Forum. Kotkaniemi added a second goal in the third period of the same game, tying the score at 4–4 en route to a 6–4 Montreal victory, and becoming the youngest player in NHL history not born in North America to score at least twice in one NHL game. He surpassed fellow Finn Patrik Laine, who, at 18 years, 183 days, recorded a hat trick for the Winnipeg Jets in a 5–4 win against the Toronto Maple Leafs on 19 October 2016. On 6 January 2019, during a game against the Nashville Predators, Kotkaniemi became the third Canadiens player to score 20 points before the age of 19. A month later on 5 February, Kotkaniemi set a new Canadiens record by becoming the first player to score goals in three straight games before the age of 19. He ultimately scored 34 points in 79 games in his rookie season. After the season concluded, Kotkaniemi underwent knee surgery to repair a chronic minor injury. He scored his first goal of the 2019–20 season in Montreal's season opener, a 4–3 shootout loss against the Carolina Hurricanes. However, on 5 December 2019, he suffered a concussion in a game against the Colorado Avalanche, resulting in eight games lost. Kotkaniemi was reassigned to the Laval Rocket, the Canadiens' AHL affiliate, on 1 February 2020.
International play
Kotkaniemi made his junior international debut for Finland at the 2017 World U18 Championships in Slovakia, he amassed 6 points in 7 games to help claim a silver medal. He returned for the following 2018 World U18 Championships in Russia, centering the top-line in recording 9 points in 7 tournament contests, helping Finland secure the gold medal over United States. He was also recognized as a top 3 on team Finland by the IIHF.