McGhee, a 6-foot-8 freshman, was injured Wednesday in an 83-72 loss at North Carolina State. Coach Donnie Tyndall announced the severity of the injury Friday after a 61-58 victory over Tennessee Tech.
McGhee is averaging 4.4 points, 3.8 rebounds and 12.9 minutes per game.
His injury adds to Tennessee's frontcourt depth problems. The Volunteers don't have a single player with a listed weight above 220 pounds.
Tennessee (5-4) already had lost one frontcourt player last week with the news that sophomore forward Dominic Woodson was transferring.