The Pelicans signed Rondo to a one-year contract during the offseason and planned to start him alongside Jrue Holiday.
Rondo is set to play for his fifth different team in the past four seasons after spending the first seven-plus years of his career with the Boston Celtics.
The 31-year-old veteran played for the Chicago Bulls last season, averaging 7.8 points, 6.7 assists and 5.1 rebounds per game in 69 regular-season contests.
During the Bulls' first-round playoff series against the Celtics, Rondo suffered a broken right thumb, and Boston went on to eliminate Chicago in six games.
Rondo is a four-time All-Star and former NBA champion (2007-08) who boasts career averages of 10.7 points, 8.5 assists and 4.9 rebounds per game.
He has led the NBA in assists per contest on three occasions, including in 2015-16, when he put up 11.7 helpers per game with the Sacramento Kings.
During Rondo's absence, the ball-handling burden will likely shift back to Holiday, who will see action alongside the likes of E'Twaun Moore, Jordan Crawford, Tony Allen, Ian Clark and Frank Jackson.