The 20-year-old Serbian international was stretchered off during the 1-0 Asia Trophy final victory over Sunderland at the end of last month.
It leaves manager Manuel Pellegrini with just two fit senior centre-backs in Vincent Kompany and Joleon Lescott, although Dedryk Boyata can provide cover.
Nastasic made 30 appearances for City in all competitions last season following his transfer from Italian side Fiorentina.
In better news for the club, striker Sergio Aguero is expected to be back training with the first team by the end of this week.
The Argentine has missed all of City's pre-season matches so far because of a knee injury, with his last match being the 5-3 win over Chelsea in New York during the club's post-season tour.
Aguero scored 17 goals in 40 appearances for City last season.