The Pelicans said the operation was to repair a core muscle injury.
Rondo was injured in the first quarter of Friday's preseason contest against the Oklahoma City Thunder.
Veteran Jrue Holiday will open the campaign as the starting point guard. New Orleans starts its season on Oct. 18 against the Memphis Grizzlies.
The 31-year-old Rondo signed a one-year, $3.3 million deal with the Pelicans in the offseason.
He averaged 7.8 points and 6.7 assists for the Chicago Bulls last season.