He did not stay and watch his teammates finish the victory, as TNT cameras showed Davis leaving the arena with his agent, Rich Paul.
Pelicans coach Alvin Gentry refused to address the situation following the contest.
"I'm going to talk about the guys who played the game," Gentry told reporters. "They did a great job. We found a way to win the game. That's what's important."
The Pelicans said after the game Davis went to get an MRI on his shoulder, per Andrew Lopez of the Times-Picayune. Ramona Shelburne of ESPN cited a source who said the MRI revealed a "muscle contusion but 'nothing too bad.'"
He will undergo treatment and make a decision whether he will play in Sunday's All-Star Game in the coming days.
Davis publicly requested a trade from the Pelicans ahead of the Feb. 7 deadline, but the team did not move him. The situation has been awkward since, and the Pelicans considered benching Davis for the remainder of the season before they agreed to allow him to play after conferring with the NBA.
The Pelicans are 2-2 since the deadline, but Davis has not been the same player. He's averaging 15.8 points and 8.8 rebounds over his last four games, including a three-point, six-rebound outing in Tuesday's loss to the Orlando Magic.
"We sucked," Davis told reporters. "Nobody was interested in playing, that's what it looked like. You play a team like that fighting for a spot, you should expect that to happen."
It's unclear how Davis or the Pelicans will handle the shoulder injury, but this is an untenable situation for all parties involved.