Following the Browns' loss, coach Hue Jackson said Kessler was considered day-to-day.
"There is nothing broken. It will be day-to-day," Jackson said. "It is a chest/rib situation and, obviously, we will find out more tomorrow."
Kessler, who appeared to be in serious pain as he spoke, said he was simply in too much pain to play, though he tried to return. Both Jackson and Kessler said X-rays came back clean.
Kessler was hurt when he landed on his right shoulder as he was smothered by Patriots linebacker Dont'a Hightower.
"I landed and I heard something weird," Kessler said in describing the injury.
Kessler lost the ball as he attempted to throw on a dropback from the Browns' 10-yard line. The ball went backward and sideways, resulting in a safety when the ball rolled out of the side of the end zone. Kessler officially was credited with a rush for no yards and a fumble.
Kessler was slow to get up, then was taken to the locker room shortly after he returned to the bench. He had guided the Browns to a touchdown -- an 11-yard throw to Andrew Hawkins -- on his second drive.
The rookie quarterback said the training staff would call him Sunday night to see how he felt before determining if he would be sent for an MRI on Monday. He said he would do all he could to play next week.
"My goal is to come back as fast as possible," Kessler said. "I'll know more in the next couple days and just see how it feels and stay on top of it and get treatment. My goal is to get healthy really fast."
Kessler, a third-round pick, had been the 26th different quarterback to start for the Browns since 1999.
Terrelle Pryor took the first two snaps with Kessler out, gaining 1 yard on a run and throwing incomplete on the second.
But in the fourth quarter, Whitehurst limped into the locker room and was replaced by Pryor. Whitehurst, hit by Jonathan Jones as he threw, suffered a left knee injury.
Whitehurst did return to the game, but he said his left knee situation would be day-to-day as he sees how it feels during the week.
"I just landed on it. I think it hyperextended," Whitehurst said. "I was hoping it wasn't serious. I think I'll be fine."
According to ESPN Stats & Information, Whitehurst's throw made the Browns the first team since the 2002 Eagles to have five different players attempt a pass in the team's first five games.
Robert Griffin III, who began the season as the Browns' starter, is on injured reserve with a fractured bone in his left shoulder. Josh McCown, who replaced Griffin, has been out since Week 1 with a broken left collarbone. McCown is scheduled to get an X-ray on Monday to see how he is healing.
"I won't know [if McCown can play] until we get some more medical reports back for him," Jackson said.