Gordon, 27, suffered the injury Saturday night in a loss to the Utah Jazz. It was the second time this season that he broke the finger on his shooting hand; he missed 16 games for the injury earlier this season.
Set to be an unrestricted free agent for the first time in his career this summer, Gordon is averaging 15.4 points, 2.7 assists and 2.3 rebounds in 45 appearances. He has yet to play more than 64 games in the regular season in his five years with New Orleans.
Tyreke Evans (right knee), Quincy Pondexter (left knee) and Bryce Dejean-Jones (right wrist) have already been ruled out for the rest of the season, and Alexis Ajinca also remains out with a fractured sternum.
The Pelicans received an injury hardship exception from the NBA, which they used Tuesday to sign shooting guard Orlando Johnson, most recently of the D-League's Austin Spurs, to a 10-day contract.
ESPN Pelicans reporter Justin Verrier contributed to this report.