The 34-year-old former Barcelona man appeared to damage a calf muscle in an awkward landing with 15 minutes of the match remaining.
He was replaced by Willy Caballero, who saw out the remainder of the goalless draw at the Etihad Stadium.
After the match, a concerned Guardiola said: "Of course he has an injury, probably [out] for some weeks.
"I don't know if he will be available again this season."
Bravo and Caballero have been competing for the number one jersey at the club this season, with the former having played 29 times this season while keeping just six clean sheets.
United legend and pundit Gary Neville was, meanwhile, unimpressed by seeing the keeper removed from the field on a stretcher, and commented: "A stretcher for a calf strain… please. Oh come on.
“He’d not done anything for 20, 25 minutes, he’d not been involved and then he’s leaped with his left leg for that catch from the last corner.
“I’m not quite sure why there’s a stretcher on. It’s a calf strain. Am I missing something? You don’t need a stretcher on for a calf strain. Please.
“He kicked the ball forward after that. Come on. I apologise if he hasn’t got a calf strain.”