It was not immediately clear how significant the injury was, but the television broadcast showed blood on a finger on his left hand. He went to the locker room following the injury, and when he returned to the sideline, he was no longer in uniform.
After the game, UCLA coach Jim Mora said team doctors made the decision to not let Rosen return but did not provide specifics about the injury.
"We felt it was best to keep him out and I respect that and I trust them and I think it was the right decision," Mora said. "We'll re-evaluate. They'll examine him tomorrow and we'll make a decision on how to move on."
Rosen was 12-of-21 for 93 yards with a touchdown before he left. He was replaced by redshirt freshman Devon Modster.
Modster was 7-of-12 for 77 yards and a touchdown in the Bruins' 44-23 loss to the Huskies.
UCLA QB Rosen leaves the game in the 3rd
Bruins quarterback Josh Rosen heads to the locker room in the third quarter with apparent hand injury.