The Argentinian will not have to undergo surgery, but his absence will likely be a huge blow to City boss Manuel Pellegrini.
Demichelis signed for Atletico Madrid on a free transfer in July after his Malaga contract expired, but he made the move to the Premier League without making an appearance, with City short of options following an injury to captain Vincent Kompany.
However, Demichelis himself is now sidelined, having yet to feature for City so far this season.
Micah Richards remains out with a hamstring injury, while Matija Nastasic is regaining fitness after missing a chunk of pre-season with an ankle injury.
Demichelis made 45 appearances for Malaga last season as they finished sixth in La Liga and reached the quarter-finals of the UEFA Champions League.
When fit, he will play under Pellegrini for the third different club, having also featured for the Chilean while at La Rosaleda and River Plate.
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