Jennifer Hale of Fox Sports NOLA reported the news.
Allen, 35, will miss his 13th consecutive game Wednesday night. He was averaging 4.7 points and 2.1 rebounds per game before being injured, playing in 22 contests.
The Pelicans have been hit with a rash of injuries throughout the season. They signed DeAndre Liggins on Wednesday thanks to an injury exemption granted by the NBA. Liggins previously played 31 games with the Milwaukee Bucks earlier this season.
Allen's latest setback could keep him out through the All-Star break if he rests through the latter half of his injury timeframe. The veteran, who is in his first season with the Pelicans after spending seven years with the Memphis Grizzlies, has missed at least 10 games in each of the last five seasons.
Jrue Holiday, Ian Clark and, perhaps, Liggins will see a majority of the minutes at the 2-guard spot moving forward.