The 26-year-old pulled up after just 10 minutes of Spain's World Cup qualifying draw with France in Madrid on Tuesday.
There were fears he could face a lengthy lay-off but manager Roberto Mancini has delivered an upbeat assessment following the player's return to Manchester.
Silva will definitely miss Saturday's Barclays Premier League clash at West Brom and Wednesday's vital Champions League encounter with Ajax but could face Swansea the following Saturday.
Mancini said: "He is not ready for Saturday, and will not be for the Champions League, but we hope for the next game against Swansea."
England players Joe Hart, Joleon Lescott and James Milner returned to City later than expected after their World Cup qualifier in Poland was put back from Tuesday to Wednesday.
Despite the disruption to his preparations, Mancini has no concerns about their condition.
The Italian said: "The English players who played on Wednesday are tired but I am not worried, they have another day to recover."
Source: PA
Source: PA