The Manchester City midfielder suffered a sprained ankle in his side's 1-0 Premier League defeat by Tottenham Hotspur on Wednesday.
"I am very sorry, I hope he can play in the World Cup," City's Italian manager Roberto Mancini told a news conference on Friday.
"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."
England coach Fabio Capello usually fields Barry in his starting line up along with Liverpool's Steven Gerrard and Chelsea's Frank Lampard.
The Italian boss will name the team's provisional 30-man World Cup squad on Tuesday before trimming it to 23 players after friendlies against Mexico and Japan.
England will start their World Cup campaign against the United States on June 12th.