The Ducks said an MRI on Saturday confirmed the tear and that surgery will be scheduled for Boucher.
A 6-foot-10 senior, Boucher averaged 11.8 points, 6.1 rebounds and a Pac-12-best 2.5 blocks this season. He missed two games in December with an ankle injury.
His latest injury is a tough blow for Oregon (29-5), which lost to Arizona 83-80 in the Pac-12 tournament championship game on Saturday night.
Boucher told ESPN.com after the loss that he didn't think he had severely injured his knee until Saturday morning.
"No, I didn't feel anything until this morning," he said. "I went to get an MRI, and they said it was [torn]. I just felt like it was moving by itself."
Boucher tried to motivate his team from the bench as the Ducks fought valiantly on an emotional night. But he said he's still not sure how to process the dramatic turn in his season.
"It's horrible," said Boucher with bloodshot eyes as he slowly walked toward the team bus outside T-Mobile Arena on Saturday night. "I'm trying not to think about it."
Just before Saturday's game, Wildcats coach Sean Miller approached Boucher and hugged him.
"God bless you," Miller told Boucher. "Wish we could see you out there."
Also prior to the contest, Miller said of Boucher: "I feel really bad for him."
Without Boucher, who is Oregon's best inside player, coach Dana Altman will have to lean more on junior forward Kavell Bigby-Williams down low.
Bigby-Williams had a double-double earlier in the season in nonconference play. But he has seen inconsistent playing time during the conference season. He had three points in 14 minutes on Saturday night.
ESPN's Myron Medcalf contributed to this report.