Buckeyes coach Thad Matta announced Tate is scheduled to have surgery on the shoulder on Friday.
"Jae'Sean is the heart and soul of this basketball team," Matta said. "We challenged our guys -- man down, you've got to man up. I hate it for Jae'Sean, but that being said, we have to go on and find a way to regroup and get ready to go again."
Tate, who at 6-foot-4 is the Buckeyes' toughest player, averaged 11.7 points and 6.4 rebounds in 28 games. He is coming off a 15-point, 12-rebound performance in a 65-62 overtime win against Nebraska on Saturday.
The Buckeyes have two regular-season games left: one against Michigan State and one at home against Iowa.