Koivu, 35, is scheduled to undergo surgery Friday. He suffered the injury after colliding with Buffalo Sabres forward Tage Thompson in the first period of Tuesday's 5-4 shootout loss and did not return.
The Finnish center is sixth on the team with 29 points this season and is averaging 18:18 of ice time per game, third among forwards. He leads the team with a 54.6 face-off percentage.
Koivu, the No. 6 overall pick in the 2001 NHL draft, ranks first in franchise history in games played (973), points (688), assists, (487) as well as power play points, short-handed points and multipoint games.
He scored his 200th career NHL goal on Jan. 21 to become the second player in team history to reach the milestone.
In a corresponding move, the Wild recalled 22-year-old Joel Eriksson Ek from its AHL affiliate. Eriksson Ek has played 36 games with Minnesota this season.
Koivu has one year remaining on his contract with a $5.5 million cap hit.
The Wild have another significant injury they're handling: Defenseman Matt Dumba is out until at least April after shoulder surgery.
Minnesota, which has made the playoffs in six consecutive seasons, has 57 points in 53 games this season and is holding on to the top wild-card spot in the West. The Wild are three points behind Dallas for the third spot in the Central Division.