Koivu served as the Canadiens' captain for ten of his 14 years with the club, making his captaincy tenure the longest in the team's history, tied with Jean Béliveau.

He also served as captain of the Finnish national men's ice hockey team from 1998 to 2010, and was inducted into IIHF Hall of Fame in 2017.

Koivu began his professional ice hockey career playing for TPS in the Finnish SM-liiga, beginning in 1992–93.

The following season, he was amongst the NHL leading scorers (13 goals and 25 assists for 38 points) before suffering a knee injury on December 7, 1996, in a game against Chicago Blackhawks.

Fans gave Koivu an eight-minute standing ovation when he skated onto the Molson Centre ice for the first time on April 9, 2002, in the team's 80th game of the season.

[6] Koivu helped the team to gain a playoff spot and they went on to beat the top-seeded Boston Bruins in six games.

For his courage and off-ice team leadership while undergoing cancer treatment, he was awarded the Bill Masterton Memorial Trophy following the 2002 playoffs.

During the 2004–05 NHL lockout, he returned to Finland to play for TPS, whose head coach at the time was his father, Jukka Koivu.

He remained out of the lineup for the rest of the series and underwent surgery to repair a detached retina during the off-season.

Waiting until the end of the season, Koivu underwent further surgery to his eye and also tried a contact lens design to counteract the cataract's effects.

[10] Early in the 2007–08 season in October, Koivu was criticized by nationalist lawyer Guy Bertrand for not speaking French in a videotaped pre-game ceremony.

[11] He replied to Bertrand's remarks that he is not perfect, and jokingly mentioned that he speaks French to his wife during intimate moments.

On October 18, 2008, Koivu moved up to seventh on the Canadiens' all-time assists list, surpassing Maurice "Rocket" Richard in a game against the Phoenix Coyotes; Koivu netted one and assisted on two from newly acquired linemate Alex Tanguay when the Habs beat Coyotes 4–1.

[15] Upon the conclusion of the 2008–09 season, Koivu tied Jean Béliveau as the longest-serving captain in team history, having held the position for ten years.

On January 22, 2011, during the 2010–11 season, Koivu made his first return to Montreal as a member of the Ducks, and was welcomed by a standing ovation.

[23] On October 24, 2013, Koivu returned to Montreal for a second time as a Duck, and was once again welcomed by a standing ovation in what would be his last game at the Bell Centre.

He was offered the captaincy but declined, pleading, "It would only stir things up and the team has already a great captain, Ville Peltonen.

The line plays mainly to the excellent chemistry Koivu and Selänne seem to have and this has also affected the NHL; after 1999 World Championships, Selänne said in an interview on a Finnish TV program, "It would be great to play with Saku," which led to speculation about Koivu being traded to Anaheim.

His younger brother Mikko is also a former ice hockey player, who played for the Minnesota Wild and the Columbus Blue Jackets.