The 29-year-old suffered the injurying during the 1-0 defeat by Tottenham on Wednesday.
The injury could affect Barry’s chances of being named in England boss Fabio Capello’s provisional 30-man squad for the World Cup.
“I feel very sorry for him,” said City manager Roberto Mancini.
“Gareth is a fantastic guy and a fantastic player.
“I don’t know exactly how bad, maybe three to four weeks. I hope he can play in the World Cup but Fabio Capello and his medical staff must decide.
“He deserves to play in the World Cup”
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As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?
Being an amiable guy is good for you and Jurgen Klopp is living proof.