Winslow was admitted to the Cleveland Clinic on Thursday. He practiced Monday but had been feeling ill for several days and the team sent him to the doctor for further tests and evaluation.
Browns coach Romeo Crennel had expected the 25-year-old player to be discharged on Friday, but team spokesman Bill Bonsiewicz said Winslow will remain hospitalized.
Citing patient privacy laws, Crennel did not provide specifics on Winslow's illness.
"His arms and legs aren't falling off or anything like that," said Crennel, adding the Pro Bowler was questionable -- 50-50 -- for Monday's game against the defending Super Bowl champions.
Crennel has spoken with Winslow, who has undergone four knee surgeries and has had to play through pain throughout most of his four-year NFL career.
"He's a competitive player," Crennel said. "We all know he has had some injuries that he has had to deal with and he's played through them, and at times we've had to manage him so that he can play through them. We know that he'll be out there [Monday] if at all possible. If it's possible that he can be there, he'll be there."
Dinkins also spoke with Winslow, whose illness is not believed to be related to any of his previous injuries.
"I don't really know what his situation is, but I hope that he plays," Dinkins said. "Obviously this is a league where you want all your best players to play. I want him out there. I hope he's fine whatever's going on with him. I hope he's back because we need him."
Winslow has had four operations on his right knee, and following one of them needed surgery after he got a staph infection. He missed 14 games in his rookie year in 2004 after breaking his leg in a game and Winslow sat out the entire 2005 season because of injuries sustained in a near-fatal motorcycle crash.
Last season, Winslow had 82 receptions for 1,106 yards.
The Browns have closely monitored his practice time, hoping to keep Winslow as fresh as possible for games. An All-American at Miami and former first-round draft pick, Winslow is obsessive when it comes to working out. He has spent countless hours in previous off-seasons rehabbing his injuries and getting himself into peak physical condition.
Despite his pain, Winslow has started in 34 of 36 games since 2006.
"Anybody who knows him understands the hard work that he puts in," Dinkins said. "A lot of people just see the outside things, but he's a great guy and anything that goes wrong with him, as a friend I want to make sure that he's OK first."