A statement on City's official website said that a scan on the 32-year-old Argentinian had revealed ligament damage but that surgery is not required.
Centre-back Demichelis only joined the Blues on a two-year contract from Atletico Madrid on Sunday.
City already had defenders nursing injuries, with skipper Vincent Kompany currently sidelined by a groin problem and Micah Richards out with a hamstring complaint.
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