It is unclear how long Davis will be sidelined.
Davis suffered the injury in the first quarter of Sunday's game against the New York Knicks. He said he hit his hand on the rim while going up to try and compete an alley-oop.
Davis had seven points and four rebounds before going to the bench with 1:32 to play in the quarter and did not return. Despite losing Davis, the Pelicans won 103-99 to hand the Knicks their ninth straight loss.
"I haven't found anything out yet," Davis said after the game. "Most definitely I hope it's a short-term thing,"
Pelicans coach Monty Williams did not have any additional information on Davis' condition.
"I know he hit his hand on the rim on the lob, but I can't give you an update," he said.
Davis has established himself as one of the top young players in the NBA in his second year in the league.
Entering play Sunday, he led the NBA with 3.9 blocks per game. He also averaged 19.6 points and 10.6 rebounds per game for the Pelicans (7-8).
Davis' player efficiency rating of 28.35 entering play Sunday was second only to Miami's LeBron James.
If Davis is out for an extended time period, as expected, New Orleans could start power forward Ryan Anderson in his place.
Ian Begley is a regular contributor to ESPNNewYork.com.