The Argentine 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 suffered the injury in training and immediately underwent scans following the incident, but that has shown that surgery will not be required.
However, the loss of Demichelis will be a blow to Pellegrini - given captain Vincent Kompany is still sidelined with a groin injury and Micah Richards is still not fully fit.
Aside from Joleon Lescott and Matija Nastasic, Pellegrini could call on Spanish midfielder Javi Garcia, or Belgian youngster Dedryck Boyata.