The Pelicans said Hill suffered a proximal hamstring tear while working out in Los Angeles and that the surgery was successful.
The team said a full timetable for Hill's return has yet to be determined.
Hill's loss will be difficult for the Pelicans, who have little depth at small forward.
Hill started 71 games for the Pelicans in 2016-17, averaging 7.0 points and 3.8 rebounds. He is entering the second season of a four-year, $48 million contract.
The 26-year-old played his first three NBA seasons with the Indiana Pacers, who picked him 23rd overall in the 2013 NBA draft. He has averaged 6.4 points and 3.3 rebounds per game in his career.
New Orleans has struggled with its depth in recent years, losing several players to extended injuries.