Browns coach Hue Jackson called the injury pretty serious, although the player was able to tweet to supporters: "Thank you everyone for your thoughts and prayers."
Poyer absorbed a crushing blindside block while covering a punt, with Tennessee's Antonio Andrews drilling Poyer in the chest and jaw area.
Poyer, 25, remained on the turf for several minutes before walking to the sideline.
He was evaluated at the stadium for a concussion and sent to hospital for further evaluation of possible concussion and an abdominal injury.
The kidney damage was discovered at the hospital.
Andrews was penalized 15 yards for unsportsmanlike conduct on the illegal blindside block but Jackson stopped short of calling the play dirty.
"Sometimes you aim at a spot and hit some other things," Jackson said.