The 20-year-old Serbia international was stretchered off with an ankle injury during a pre-season game against Sunderland in Hong Kong last month and the club announced on their website that he will be sidelined for "four to six weeks".
England international Joleon Lescott is likely to deputise alongside captain Vincent Kompany in the absence of Nastasic, who quickly became a first-team regular after arriving from Fiorentina last year.
There was better news about striker Sergio Aguero, who is due to return to full training this week after missing City's entire pre-season programme with a knee injury.
City tackle Arsenal in a friendly in Helsinki on Saturday before kicking off their Premier League campaign at home to Newcastle United on August 19.
Manchester City lose Matija Nastasic for up to six weeks
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