Davis injured the finger in the fourth quarter but briefly returned.
The five-time All-Star will re-evaluate the injury in three-to-four days and will decide if he needs to see a hand specialist, Davis' agent Rich Paul told The Athletic's Shams Charania.
It will be a crucial stretch without Davis for the Pelicans, as the team has dropped three of their last four contests and sit four games out of a playoff spot.
The 25-year-old is averaging career highs in points (29.3), rebounds (13.3), assists (4.4), and steals (1.7).
The Pelicans (21-25) have lost four of five games without Davis this season.