Bacot came down on an Ohio State defender's foot and appeared to roll his ankle at the 12:48 mark of the first half after tipping in a rebound. He immediately went to the floor in pain after the play and had to be helped off the court by teammates.
"It was swollen by the time he got to the locker room," coach Roy Williams said. "My guess is he'll be out a while."
The 6-foot-10 Bacot was averaging 11.7 points and 9.6 rebounds, and was coming off his best game of the season, putting up 23 points, 12 rebounds and 6 blocks in North Carolina's 78-74 win over Oregon last week.
He had 2 points, 4 rebounds, a block and a steal before exiting against the Buckeyes.
The Associated Press contributed to this report.