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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The Portuguese legend has headed home from the World Cup in Russia but there is no doubt he made his mark.
Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.