Zeller was injured in the third quarter of Wednesday's 101-87 loss to the Golden State Warriors.
The Hornets said Zeller is evaluating his treatment options. The fourth-year veteran is averaging 7.2 points and 5.5 rebounds per game this season.
Charlotte will also be without forward Frank Kaminsky for Friday's game against the Chicago Bulls. Kaminsky sprained his right ankle in the second quarter Wednesday and was seen leaving the arena in a walking boot after the game.
Kaminsky, who is averaging 10.6 points, is considered day-to-day.