Bills spokesman Scott Berchtold said he was informed by the team's medical staff the player went into surgery at a Buffalo hospital at about 8 p.m. Berchtold said he had no further information, and didn't know whether Everett had shown any signs of movement since he was driven off the field in an ambulance.
General manager Marv Levy said doctors informed the team that it's too early to determine the severity of the injury and that they will know more after monitoring the player overnight.
"Certainly, we feel the injury is serious, but I don't want to speculate, and that's what the doctors told us," Levy told The Associated Press. "They told us to wait to hear from them before making any speculative announcement."
Coach Dick Jauron said immediately following the game that the player sustained a cervical spine injury, but wouldn't discuss the severity of the injury.
Everett's agent, Brian Overstreet, was not immediately available for comment.
Everett fell to the ground and never moved after a helmet-to-helmet hit when he tackled Denver's Domenik Hixon during a kickoff to open the second half. Everett was placed on a backboard with his head and body immobilized, and carefully loaded into an ambulance at the Broncos 30.
The game was delayed for about 15 minutes, and the Bills gathered at the sideline while doctors attended to the player.
Everett's injury cast a pall over the Bills following a season-opening 15-14 loss, with several players expressing concern about their teammate.
"It was real hard," cornerback Terrence McGee said. "I watched the whole thing and he never moved. ... It's real sad to see him go off on a stretcher, but we hope he's OK."
"It's real sad," added receiver Roscoe Parrish, who played with Everett at the University of Miami. "When something like that happens to a close friend of yours, and you know how much he loves football, it bothers you."
Denver players expressed concern, including kicker Jason Elam, who kicked the winning field goal as time ran out.
Before taking questions after the game, Elam said: "What we heard is not good, so for our whole team, our prayers go out to him."