Cousins hurt his ankle in Friday's 117-107 loss to the Houston Rockets and experienced soreness after the game that lingered into Sunday, keeping him out of a morning shootaround in Denver.
"He doesn't feel comfortable enough to go out there," Pelicans coach Alvin Gentry said. "There's no way we're going to stick him out there and risk further injury for one game. We'll sit him out and see what happens tomorrow."
The Pelicans are 30-42 overall and five games behind the Nuggets for the eighth seed in the Western Conference with 10 games to play, with two more to come against the Nuggets.
Cousins missed a home victory over the Rockets on March 17 because of left knee soreness and a rib contusion, and another on March 1 against the Detroit Pistons because of an automatic one-game suspension triggered by his 18th technical foul of the season.
The 26-year-old is averaging 22.5 points, 11.7 rebounds and 3.4 assists in 13 games since his trade from the Sacramento Kings during the All-Star break.
New Orleans recalled rookie Cheick Diallo from the D-League's Greensboro Swarm before Sunday's game.