The Pelicans confirmed in a statement that the 19-year-old had undergone "successful" arthroscopic surgery on a torn right lateral meniscus.
It is estimated that Williamson will return in six to eight weeks.
The 19-year-old sensation picked up the injury during the preseason and missed the Pelicans' final warm-up game.
He was named the Associated Press men's college basketball player of the year last season as he averaged 22.6 points and nine rebounds in 33 games during his one season with Duke.
Williamson has suffered knee injuries before, sustaining a knee sprain when his shoe split in half while planting his foot, causing him to miss a few weeks of action.
The 6-foot-7 Williamson is seen as the new face of the Pelicans franchise having been drafted first overall, after wantaway forward, Anthony Davis, was traded away and paired with LeBron James at the Los Angeles Lakers.
Williamson had shown flashes of his athleticism and skills during the preseason, with high-flying dunks and blocks on show, as he averaged 23.3 points for the Pelicans.
The 2019-20 NBA season starts on Tuesday, Oct. 22 as the Pelicans travel north of the border to face the reigning champions, the Toronto Raptors.
Davies and James will match up against the newly-acquired, reigning MVP, Kawhi Leonard, and Paul George as the Lakers take on the LA Clippers at the Staples Center in an opening night double-header.