Carter, a 6-foot-8 sophomore, is tied for the ACC lead in rebounding at 9.3 per game. He averages 10.3 points.
Sources told ESPN.com that Carter will likely miss the next month, which could be a significant hit to Georgia Tech's postseason hopes.
The Yellow Jackets (9-4) have lost to Dayton, Ole Miss, St. John's and Vanderbilt and are long shots to earn a bid to the NCAA tournament.
However, with a solid showing in the ACC, they could become an NIT team.
"He's a tough kid, and this hit him pretty hard," coach Brian Gregory said in a statement. "He's done everything we've asked of him this year. He's changed his body, he's become more aggressive on the glass, and his stats clearly show that he was having a tremendous sophomore season for us. He's a big part of what we do both offensively and defensively."
Georgia Tech opens conference play Saturday at Maryland (9-5, 1-0).