Cobbins was hurt in the No. 6 Cowboys' 92-66 victory against Robert Morris on Monday night. He hobbled off the floor just three minutes into the game and did not return.
"Our thoughts are with Michael, and we pray for a successful recovery," coach Travis Ford said in a statement. "We know Michael will work extremely hard and be back next season, better than ever!"
Teammate Markel Brown tweeted: "I hate it had to be him."
The 6-foot-8 Cobbins is the key to the Cowboys' low-post defense, leading the team with 19 blocks and averaging 4.5 points and 4.3 rebounds.
"Nobody is going to sit around and feel sorry for us," Ford said. "We can all be sad for Michael, and we should be, and hold our head down for him. But we don't need to hold our head down for our team.
"Everybody's going to have to step it up. And we've got some options. We've got some guys who can do some things. It may not be a big guy, but it may be somebody else having to do something. And that's the way we'll approach it if that's the case."
Kamari Murphy could move into the starting lineup to replace Cobbins as the Cowboys begin Big 12 play Saturday at Kansas State.
"We've switched up lineups in practice, so we're kind of used to playing with different guys," guard Phil Forte told The Oklahoman. "It's not too much of a difference. We have a lot of versatile players, too.
"With Mike going down now, I think that's going to be key for us."
Information from The Associated Press and The Oklahoman is included in this report.