Linebacker Karlos Dansby said that Austin has a lacerated kidney, and that he's talked to receiver a few times since he's been hospitalized.
"That's tough," Dansby said. "It's very dangerous. I'm glad they're all the precautions they need to take to get him back healthy and get him back here.
"His spirits are high. He's bummed that he can't finish the season because there's so much on the line. He's a great teammate and one hell of a competitor."
Quarterback Brian Hoyer said he had reached out to Austin as well.
"I don't think you could term this something at this point that's serious or critical," Pettine said Wednesday. "They're being very precautionary with him having to travel."
Neither Pettine nor the team disclosed the nature of the kidney issue, but it was significant enough that he was taken by ambulance from Ralph Wilson Stadium to the hospital Sunday after the Browns' loss to the Bills.
The Browns placed Austin on injured reserve Wednesday, ending his season.
Austin's wife, Stacy, was at the game and stayed in Buffalo to be with her husband. Pettine said he and several players had reached out to him at the hospital.
"He's obviously bummed," Pettine said. "But he's in as good of spirits as he can be."
Austin, who drew significant and heartfelt praise from Pettine, had 47 receptions for 568 yards and two touchdowns this season.
"It's really unfortunate, because he was a guy that really embodies what we're trying to build here," Pettine said. "How guys handle themselves on and off the field, how they interact with teammates and with the staff, and just their level of play. How they approach the game. Everything A to Z.
"We couldn't have asked a guy to come in and be a better example for our young players while at the same time being a very productive member of our receiving corps as well."
The Browns on Wednesday also signed running back Shaun Draughn. The 5-foot-11, 205-pounder in his second NFL season out of North Carolina.
The Associated Press contributed to this report.