Covington, who was carried off on a stretcher and taken to Jefferson Hospital after he was inadvertently struck in the head by Grant's right foot, entered the league's concussion protocol and will not play in Saturday's game against the Detroit Pistons.
Grant also was tested for a concussion, results of which were unknown.
Covington appeared to acknowledge the crowd as he was being carted into the locker room, and he heard supportive cheers from the fans at Wells Fargo Center after the scary scene.
While trying to contest a shot, Grant made contact with Brooklyn point guard Donald Sloan, who passed to Thaddeus Young down low. Grant's right leg whipped in the air, drilling Covington in the process.
Grant then fell on the court and might have hit his head on the hardwood before Young fell backward onto the Philadelphia forward's head after missing his layup attempt.
ESPN Staff Writer Mike Mazzeo contributed to this report.