The club says an MRI has revealed cartilage damage in the knee.
The 7-foot Smith has played in 31 games and has started 27 times. He's averaging 9.7 points, 5.8 rebounds and 1 block in 26.8 minutes per game.
The injury is only the latest setback for the Pelicans, who'd lost seven straight entering Saturday night's home game against Golden State.
New Orleans is also without leading scorer Ryan Anderson, who has a herniated disk, and starting point guard Jrue Holiday, who has a stress fracture in his right shin. Meanwhile, it is not clear if guard Tyreke Evans is ready to return from a left ankle sprain against the Warriors.