The Argentina international signed for City over the weekend after finalising a move from Atletico Madrid, a club he never actually played for following an earlier summer switch from Malaga.
The 32-year-old was reunited with his former boss Manuel Pellegrini, who will be disappointed to learn that he is unlikely to be able to use him until November.
Demichelis immediately underwent scans after suffering ligament damage and they have shown that surgery will not be required.
However, the loss of Demichelis will be a blow as City's defensive resources are already under strain with captain Vincent Kompany sidelined with a groin injury and Micah Richards still not fully fit.
Aside from Joleon Lescott and Matija Nastasic, Pellegrini could call on Spanish midfielder Javi Garcia or Belgian youngster Dedryck Boyata.