The Mets provided an update on Pillar on Tuesday, saying the outfielder suffered multiple nasal fractures and will meet with a facial specialist in Atlanta to determine the next steps.
Pillar tweeted after the game that he's recovering well following a trip to the hospital.
Pillar took a 94-mph fastball from Braves reliever Jacob Webb to the nose. Players on both teams were shaken up afterward.
The veteran was down and bleeding for some time, but he was able to get up under his own power to leave the field.
"This guy's a warrior," Rojas said postgame, according to Deesha Thosar of the New York Daily News. "He shows up every day to play hard. He got up on his feet and left.
"There was no chance I thought he was going to be able to do that after he got hit in the face. But he got up, and he left, and that's at least one positive to see in the scary moment."
Khalil Lee pinch ran for Pillar and took over in right field.
If he's out for any amount of time, it will be yet another injury to the team's already-depleted outfield.
New York placed Michael Conforto on the injured list alongside Jeff McNeil earlier Monday. The pair joined Brandon Nimmo, Albert Almora Jr., and occasional left fielder J.D. Davis, all of whom were already sidelined with various ailments.