Okafor left Sunday's preseason game against the Chicago Bulls late in the fourth quarter with the injury. He underwent an MRI on Monday that confirmed the nature of the injury.
Okafor had eight points in 17 minutes on 4-of-7 shooting against the Bulls.
Okafor joined New Orleans in August as a free agent with a two-year deal that includes a team option in the second season. The Pelicans were Okafor's third team since December, when Philadelphia traded him to Brooklyn.
Okafor, the third overall pick in the 2015 NBA draft, had worked over the summer to remake his jump shot, and he has been given the opportunity to earn minutes with the Pelicans.
Okafor, 22, made the NBA All-Rookie team in 2016 before his role increasingly diminished with the 76ers, leading to his trade to the Nets. In limited minutes for the Nets, Okafor averaged 6.4 points per game. As a rookie with the Sixers in 2015-16, Okafor averaged 17.5 points and 7 rebounds.