Barry faces four weeks out
City coach Roberto Mancini on Friday said Barry had suffered a sprained ankle and would be looked after by England's medical staff once the Premier League season finished on Sunday.
"I am very sorry, I hope he can play in the World Cup," Mancini told a news conference.
"He's a fantastic guy and fantastic player. I still hope he will play in the World Cup, but the England team will decide this.
"He will be out for three to four weeks. I don't know, but I really hope he recovers in time."
Barry limped out of City's defeat by Tottenham Hotspur on Wednesday and underwent a scan after the game.
The World Cup starts in South Africa on June 11.