The injury comes with the Pelicans in a tight battle for the No. 8 playoff spot in the Western Conference.
Davis is averaging 24.6 points and 10.4 rebounds per game. Entering Thursday's game, New Orleans was a half-game behind No. 8 Oklahoma City and 2 1/2 ahead of Phoenix.
Coach Monty Williams said before the game that the injury occurred during routine drills. Williams said Davis may have stepped on Ome Asik's foot.
Williams said it was too soon to say whether Davis would be able to play at Golden State Friday night.