Cervelli will undergo surgery on Saturday at New York-Presbyterian Hospital under the supervision of hand specialist Dr. Melvin Rosenwasser.
"It's disappointing. I know it's really disappointing for him because of all that he's been through to get to this point," manager Joe Girardi said.
Nova told the Yankees that he was feeling some stiffness in the second inning, but he convinced Girardi and pitching coach Larry Rothschild to allow him to return to the mound in the third.
He hit No. 9 hitter Munenori Kawasaki with a curveball and allowed a single up the middle to Davis, grimacing after his final pitch.
"He talked about it a little bit after the second inning and said he wanted to go back out there and try," Girardi said. "We saw the first two hitters in the third and just decided. We went out there and asked him, and he said he wasn't OK."
Visited by head athletic trainer Steve Donohue, Nova nodded to acknowledge the discomfort and rolled the ball in his fingers before handing it to Girardi.
Girardi believes the pain was above Nova's right elbow in the triceps area; neither Nova nor Cervelli was available to speak to reporters after the game.
Nova permitted two runs and four hits in two-plus innings and was relieved by David Phelps, who allowed a run over four innings with nine strikeouts and could step into Nova's rotation spot.
"My last two outings have both been on his day," Phelps said. "I was at  pitches today. It's not my decision, but if that's what they want me to do, I think I can do it."
Chris Stewart replaced Cervelli behind the plate, and Austin Romine was removed mid-inning from Triple-A Scranton/Wilkes-Barre's game against Syracuse. Girardi anticipates that Romine will be added to New York's roster for Saturday's game.
Cervelli had been on a solid run after spending most of last season in the Minors. He hit his third home run of the year in Thursday's 5-3 win over the Jays, one shy of his career high, and will hit the disabled list batting .269.
"My heart goes out to him," Girardi said. "It's going to make him stronger, and it's going to make him better. He's going to have to wait a little while to play, but we'll get him back."
Girardi was not yet certain how he would split catching duties between Stewart and Romine.
"I'll just kind of play that by ear every day," he said. "We'll have some day games, long trips. It seems like when we come home from trips, it's three or four o'clock in the morning. We'll see how Romine does."
The calamitous evening continued a year-long rash of injuries for the Yankees, who began the season with stars Derek Jeter, Alex Rodriguez, Curtis Granderson and Mark Teixeira on the disabled list.
The bench was also short one player on Friday because Kevin Youkilis continues to battle discomfort in his lower back and was not considered to be available.
Youkilis has not played since April 20, in Toronto. If he is not able to play on Saturday against Toronto left-hander J.A. Happ, he could become another candidate for the disabled list.
"Injuries are part of the game, it's part of life," Girardi said. "I'm sure everyone in here can attest that life doesn't go exactly as we want it sometimes. But that's part of it."