The 6-foot-4 Allen, whose injury was announced on Tuesday, has appeared in 22 games for New Orleans this season, averaging 4.7 points and 2.1 rebounds in 12.4 minutes per game.
Allen fell to the court during the first half of the Pelicans' victory over Philadelphia on Sunday night. He picked himself up and limped on his own to the locker room.
Allen was acquired by New Orleans as a free agent this past offseason.
The 14-year veteran has averaged 8.1 points and 3.5 rebounds in his career, which has included multiyear stints with Boston and Memphis.