The centre-back was stretchered off in the second half of Saturday's Asia Trophy final win over Sunderland following an innocuous-looking incident involving Emanuele Giaccherini.
City doctors will now assess Nastasic when they return to Manchester after the weekend and the club will hope for good news ahead of the start of the new Premier League season in three weeks.
City boss Manuel Pellegrini confirmed that the pitch - which resembled a bog - was not to blame for the centre-back's injury.
"He has at the moment (a problem with) his ankle. But we don't know how long it will be," he told Sky Sports.
"The doctor has to see him tomorrow when we arrive back in Manchester.
"I am concerned but it's better to wait. It wasn't the pitch though. He got a kick on his ankle but it was just part of the game."
Meanwhile, Pellegrini was pleased to win the Asia Trophy, where they defeated South China before Sunderland in Hong Kong, and secure his first piece of silverware since taking over.
The success also allowed City to bounce back from earlier pre-season losses to Supersport United and AmaZulu FC in South Africa.
Pellegrini said: "I think it is important for us, because, here in Hong Kong, we improved on what we did in South Africa.
"Not only because we won here but because the team in each game is playing better in the way I want."