The defenseman was injured in the third period of a 5-1 loss to the Colorado Avalanche at Xcel Energy Center on Saturday when he was hit by Wild forward Jordan Greenway.
"You guys all saw it. Obviously doesn't look good, but who knows how long (he'll be out)," Minnesota coach Dean Evason said.
Dumba will miss at least the next four games, beginning against the Avalanche on Sunday (8 p.m. ET; NHLN, FS-N, FS-WI, ALT, NHL.TV). He has scored four points (three goals, one assist) in nine games and is fourth on the Wild in average ice time per game (21:24).
"He's a big part of our team," Greenway said after the game Saturday. "He has a big impact out there, so it's always tough losing a guy like that."
Wild forwards Marcus Johansson, who left in the second period Saturday with an undisclosed injury, and Marcus Foligno, who was placed in the NHL COVID-19 protocol Sunday, will not play Sunday. Minnesota recalled forwards Luke Johnson, Gerry Mayhew and Kyle Rau from the taxi squad.
"We're still in the NHL, we're still playing, right?" Evason said. "We've got a roster, we've got a hockey club, and when that puck drops, we're going to compete our [butts] off."
NHL.com independent correspondent Jessi Pierce contributed to this report
