Koivu suffered the injury during the Wild's 5-4 shootout loss Tuesday to the Buffalo Sabres. The 35-year-old forward collided with Sabres forward Tage Thompson in the first period.
Koivu will have surgery to repair his knee Friday.
The All-Star center recorded 29 points (eight goals, 21 assists) in 48 games with the Wild this season. He ranked 14th in the NHL with 488 faceoff wins, which led the Wild.
Minnesota selected Koivu with the sixth-overall pick in the 2001 NHL Draft. Koivu leads the franchise in games played, points, assists, shots, power-play points, game-winning goals and short-handed goals.
Koivu has 688 points (201 goals, 487 assists) in 973 career NHL games. He has played in 14 seasons, all with the Wild.
Minnesota (26-22-5) hosts the Edmonton Oilers (23-25-5) on Thursday night. The Wild sit at fourth place in the Central Division with 57 points.