The midfielder's last Premier League game was for Arsenal in 2005 before joining Juventus. He then moved on to Inter Milan, from where he joined City.
"I suffered the injury in the last Inter game and didn't realise it was that bad," he told the City website.
"I look forward to getting a run of games in the Premier League."
City's next two Premier League games are away to Hull and at home to Bolton, before they host Stoke in the FA Cup.
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Vieira, who is still captain of France, spent nine years at Arsenal during which time he won three league titles and four FA Cups, before moving to Italy.
The 33-year-old spent only one season at Juventus before City boss Roberto Mancini signed him for Inter Milan.
There, he won two Italian league titles under Mancini and a third under Jose Mourinho, but in that third season he made only 16 appearances, most as a substitute.
And having played for teams who have been regular challengers for trophies, Vieira said he felt he had found more of the same at City.
"I have found a team that matches my expectations," he said.
"I think the future for this club is fantastic. There are a lot of winners and great players in the dressing room.
"Hopefully we can achieve what we want and finish in the top four. We are getting closer to Manchester United. The gap is definitely narrowing."
Source: BBC Sport
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