The 20-year-old Serbia international, who impressed during his first season in England, was stretched off in the win over Sunderland in a pre-season tournament in Hong Kong last month.
He is expected to be sidelined for another four to six weeks, the club said on its website (www.mcfc.co.uk).
Striker Sergio Aguero is expected to return to training by the end of week, having missed pre-season training with a knee injury.
City open their Premier League campaign against Newcastle United on August 19.
Image: Matija Nastasic
Photograph: Robert Cianflone/Getty Images
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