Paul will start rehabilitating immediately and be on crutches for two or three weeks, the team announced.
He will miss the Feb. 14 All-Star Game at Cowboys Stadium in Arlington, Texas.
"Obviously this is a tough thing for me," Paul said in a statement. "I have been fortunate through my career as a basketball player to not have suffered many injuries. The main thing is for me to get back healthy and to help this team however I can."
Paul was injured Jan. 27 against Golden State, then aggravated the injury when he collided with a camera while chasing an errant pass in the final seconds of regulation against the Chicago Bulls last Friday.
New Orleans (26-23) is in danger of missing the playoffs for the first time in three years. The Hornets have lost three consecutive home games and are in last place in the Southwest Division, two games out of the eighth and final playoff spot in the Western Conference.
Paul sat out eight games earlier this season with a sprained ankle. New Orleans is 5-6 when he does not play.