Koivu began the 2023–24 season with the TPS U18 team, but moved up to the
U20 team as the season progressed, where he played the majority of the season. Koivu recorded 16 goals and 15 assists for 31 points in 28 regular season games, making Koivu the leading goal scorer and third-highest point scorer for TPS. In the playoffs, Koivu recorded two goals and five assists for seven points in 10 games. Koivu made his Liiga debut on 3 January 2024, in an away game against
Mikkelin Jukurit. Koivu earned a spot in the TPS lineup following several team injuries. Koivu was designated as the third-line center, playing with U20 forwards
Kasper Pikkarainen and
Jan Shikera. Koivu recorded 13:37 of ice time with a −2 rating and won 52.9% of 17 faceoffs. The
Montreal Canadiens drafted Koivu in the third round as the 70th overall pick in the
2024 NHL entry draft. Koivu's father
Saku was also drafted by the Canadiens in the summer of 1993. They became the second father-son pair in franchise history to be drafted by the club, after the Canadiens selected
Réjean Houle first overall in 1969 and his son
Jean-François 99th overall in 1993. Koivu scored his first career Liiga goal during the ninth round of the 2024–25 season on 28 September 2024, against
Ässät. During the rookie season, Koivu played 32 regular season games with one goal and seven assists for eight points and two playoff games without points. Koivu also played part of the season with the TPS U20 team. Koivu tied for the team lead in playoff goals with five. ==International play==