The 25-year-old was forced off within the first minute of England's 2-0 win at Wembley and is expected to miss Champions League ties against Juventus and Borussia Moenchengladbach and a League Cup clash against Sunderland.
He could also miss Premier League matches against Crystal Palace, West Ham United, Tottenham Hotspur and Newcastle United and England's remaining Euro 2016 qualifiers against Estonia and Lithuania.
On a more positive note for City, Brazilian midfielder Fernando is closing in on full fitness after recovering from a groin injury that he battled with for most of last season.
The 28-year-old last featured for his club on May 10 and said he needed pain-killing injections before most of his 33 appearances.
"I've been working hard to recover. I'm feeling much better now with no pain so I will resume normal training this week and hopefully be available at some point within the next fortnight," Fernando told the club website.
"I can't wait to get my season finally up and running and being pain free at last will be a huge relief," he added.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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