In a statement, the Hornets said Zeller had successful surgery on the fourth metacarpal of his left hand. He had the procedure performed by Dr. Michelle Carlson at the Hospital for Special Surgery in New York.
The Hornets said Zeller will be listed as out and will be reevaluated in four weeks, leaving Charlotte without its starting center for an extended period.
In Zeller's absence, the Hornets could slot backup center Bismack Biyombo into the starting lineup. Charlotte also has an open roster spot to potentially add a player.
Zeller posted career-best averages of 11.1 points and 7.1 rebounds per game last season.
Charlotte selected Zeller with the No. 4 overall pick in the 2013 NBA Draft out of Indiana. In 420 career games (253 starts) with the franchise, he has averaged 8.6 points and 5.9 rebounds.