The team said Nance is expected to miss four to six weeks.
Nance, who also dealt with an ankle injury during the preseason, previously missed four games with the injury but returned to play Nov. 22. He missed Wednesday's game against the Philadelphia 76ers with an illness.
In 14 games this season, Nance is averaging 3.5 points and 4.1 rebounds per game in 15.1 minutes but has been a valuable asset to the Pelicans in the locker room.
According to Spotrac tracking data, the Pelicans had players miss a combined 64 games this season because of injury, tied for fourth most in the league.
Even with Nance's absence, there's reason for optimism surrounding the health of the rest of the roster.
Veteran guard CJ McCollum returned against the Sixers after missing 12 games with a punctured lung, and third-year forward Trey Murphy III plans to make his season debut Friday against the San Antonio Spurs, sources told ESPN's Adrian Wojnarowski. Murphy also hinted at his return on his social media accounts.
New Orleans is 10-9 this season but did reach the quarterfinals of the NBA's in-season tournament. The Pelicans will travel to take on the Sacramento Kings on Monday.