The Hornets confirmed Monday night that Zeller will have surgery but did not provide a timetable for his return.
He will undergo surgery on Tuesday in Los Angeles, sources said. Zeller suffered the injury against Golden State last Wednesday in Charlotte.
Zeller is in the first season of a four-year, $56 million contract. He is averaging 7.2 points and 5.5 rebounds per game this season. With the arrival of Dwight Howard, Zeller moved into a backup role.
Charlotte (9-16) has struggled with several injuries, including a leave of absence by coach Steve Clifford, who is dealing with a health situation.
Zeller was the No. 4 overall pick in the 2013 NBA draft.