The Pelicans say Holiday had the procedure done in Philadelphia on Tuesday by Dr. William Meyers, who is known as a sports hernia specialist.
The club says the typical timetable for recovery is about six weeks, which would take Holiday beyond the end of the regular season.
Holiday already has missed the past eight games with a strained abdomen. The Pelicans are eliminated from playoff contention.
This season has been among Holiday's best. The 10-year veteran averaged career highs of 21.2 points and five rebounds per game, tied his career high for steals per game with 1.6 and had his third-highest assist average at 7.7.