LaVine, who was averaging 18.9 points, 3.4 rebounds and 3.0 assists, will have surgery at a later date, the team said.
He tweeted Sunday that he considers this a "minor setback but I'll be back stronger than before."
LaVine is part of Minnesota's young trio of 21-year-olds that includes Andrew Wiggins and Karl-Anthony Towns. It is a group that has given the team's long-suffering fans hope that the franchise is returning to relevance. LaVine's explosive athleticism has made him a crowd favorite, and he had taken another step this season toward proving he is more than just a dunker.
LaVine was shooting 38.7 percent from 3-point range and had worked harder to become a better defender under new coach Tom Thibodeau. After winning the past two dunk titles, LaVine recently decided not to go for a third straight win this year, a decision Thibodeau said proved the flashy youngster had the bigger picture in mind.
"He's made himself into one of the best 2-guards in the league," Thibodeau said Saturday. "His overall game has really blossomed. He's shooting the 3 great. The free throws, the drives, all of it. So he'll get through it. He's a mentally tough kid. And as I mentioned, he's already talking about what's next."
Towns said he was moved to tears when he heard the news.
"That's not just my teammate -- that's my brother. That's one of my best friends," Towns said. "For him to have to go through that, it hurts me a lot. I'm just wishing him a speedy recovery."
Don't know you personally but love your talent homie. Have a healthy and speedy recovery @ZachLaVine!! Minor set back/major comeback.— LeBron James (@KingJames) February 4, 2017
Thibodeau said veteran Brandon Rush will start in LaVine's place. Rush played well when LaVine missed two games in January with a hip injury. The Wolves beat Houston and Oklahoma City with Rush in the starting lineup.
"He was having a career year," Rush said. "I feel for him. He's just got to put the work in to get back."
Few doubt LaVine there. He is one of the team's hardest workers, having logged long hours at the team's practice facility to work on his jumper and add muscle to a lean frame.
"He's been in great spirits all day," Towns said. "I see him coming back with even more bounce than he had before he got hurt. He'll be able to jump even higher, which is ridiculous to think about."
After the Wolves started the season a disappointing 6-18, they showed signs of putting things together. Improved defense and more consistent ball movement helped them go 13-11 before losses to Cleveland and Detroit this week. They had climbed to just two-plus games back of the eighth seed in the West before those two losses, and LaVine was starting to pull himself out of a shooting funk that had set in since he missed two games with the hip injury.
Thibodeau has a few options to help the team weather LaVine's absence. Among them: Wiggins could move from small forward to shooting guard and Nemanja Bjelica could start at small forward, a strategy the coach used when LaVine missed a game against the Los Angeles Lakers early in the season.
The Wolves already have an open roster spot after waiving John Lucas III earlier this season. They are expected to fill it shortly with a 10-day contract to give them some more depth.
"You don't replace a player like Zach individually," Thibodeau said. "You have to do it collectively."
The Associated Press contributed to this report.