Davis suffered the injury late in the fourth quarter of Friday's 128-112 loss to Portland. He had his fingers taped together and played briefly before exiting with 1:18 left to play. He finished with 27 points and seven rebounds.
Davis had an X-ray after the game, a team official told reporters.
For the season, Davis, a five-time All-Star selection, is averaging 29.3 points, 13.3 rebounds and 2.6 blocks per game -- all above his career averages. He has missed five games due to injury and illness this season.
The Pelicans have lost three of four to drop to 21-15, four games behind the Los Angeles Lakers for the eighth and final playoff spot in the Western Conference entering Saturday's games.
New Orleans next faces Memphis on Monday night to conclude a five-game road trip. The Pelicans have four games next week and a total of seven during the two weeks that Davis could miss.
The Associated Press contributed to this report.