The 32-year-old Argentine centre-back only arrived from Atletico Madrid on Sunday.
After injuring himself in training, he underwent a scan that revealed ligament damage, but a statement on the City website said that surgery would not be necessary.
"A knee injury sustained in training is set to keep new arrival Martin Demichelis out for around six weeks," read the statement on www.mcfc.co.uk.
"The club doctor confirmed a scan last night (Thursday) revealed ligament damage, but that surgery is not required."
Demichelis's absence adds to manager Manuel Pellegrini's problems in defence, with captain Vincent Kompany currently sidelined by a groin problem and Micah Richards unavailable due to a hamstring complaint.
Manchester City new boy Martin Demichelis out for six weeks
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