Davis suffered the injury during the second quarter of Wednesday night's loss to the Dallas Mavericks.
The team's leading scorer and rebounder was holding the shoulder on his way to play defense and didn't return after leaving the game during a New Orleans timeout with 4:13 left in the first half.
He was on the bench during the second half with his left arm in a sling.
"When you play as hard as AD and these guys who go after it every single night, they're going to have bumps and bruises,'' Pelicans coach Monty Williams said after the game.
Davis, 20, averages 20 points and 10 rebounds per game and leads the NBA in blocked shot. He made his first All-Star appearance this season despite missing seven games in December due to a broken hand.
"It's difficult, but guys have been in and out all year,'' Pelicans guard Eric Gordon said. "We've just got to keep on adjusting.''
The Pelicans visit the Phoenix Suns on Friday night.
Information from the Associated Press was used in this report.