The 33-year-old defenseman was injured during a 4-1 loss to the Dallas Stars on Saturday. He will have surgery at a date to be determined.
The Wild are 44-25-10 following their 3-0 win against the Edmonton Oilers on Monday. The victory moved them five points ahead of the Colorado Avalanche for third place in the Central Division.
"I just feel real bad for him," Wild coach Bruce Boudreau said. "He's a guy that's been really durable his whole life. It's probably pretty depressing for him, but we just want him to get better."
Suter had 51 points (six goals, 45 assists) in 78 games this season and ranks second in the NHL with an average of 26:46 of ice time per game, behind
Drew Doughty
of the Los Angeles Kings (26:47).
Defenseman Carson Soucy made his NHL debut Monday. The 23-year-old was a fifth-round pick by the Wild (No. 137) in the 2013 NHL Draft. Minnesota is also without defensemen Jared Spurgeon (hamstring) and Gustav Olofsson (concussion).
"I think it's tough, especially with Suter and [Spurgeon] out, but then the other guys have to step up," Wild defenseman Jonas Brodin said.
NHL.com correspondent Jessi Pierce contributed to this report.