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 tomorrow [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."
Mancini also has no worries about Hart's state of mind ahead of his return to action with City.
A fortnight after being widely hailed as the best goalkeeper in the world after a stunning display against Borussia Dortmund, Hart was criticised for an error that allowed Poland to score on Wednesday.
Mancini said: "I think this is a situation that happens when you can play but usually Joe saves everything."
There have also been rumours in recent days suggesting midfield talisman Yaya Toure might want to leave the Etihad Stadium for a new challenge, but Mancini was dismissive.
The Italian believes the 29-year-old Ivorian can achieve can continue to get all he wants with City.
Mancini, speaking to media to preview the West Brom game, said: "Every day we have a new challenge here. In two-and-a-half years we won the FA Cup, the Premier League, the Community Shield.
"Now we need to win other cups and other Premier Leagues. We need to work more for this challenge. I think Yaya thinks like me and the other players.
"I am happy Yaya wants a new challenge, I also want a new challenge. I want to win the next game, then the next game in the Champions League. We want to do everything together."
Mancini has certainly welcomed suggestions Toure might want to sit out next year's African Nations Cup.
Toure's absence during last season's tournament coincided with the champions' worst spell of the campaign.
Mancini said: "I didn't speak with Yaya about this. Hopefully we will speak in the next week. I hope he stays here but I don't know."