The Argentina striker was forced off moments after scoring the third goal at the Etihad Stadium from the penalty spot in the 74th minute. City do not expect to know the extent of the injury until at least Thursday but first-team coach David Platt has already ruled out the possibility of Aguero facing Watford in the FA Cup on Saturday.
Last season's top scorer could also be doubtful for the January 13 trip to Arsenal. Platt said: "It is difficult to assess an injury like that, how long it is going to be. He'll certainly be out Saturday and in my experience he'd be doubtful for Arsenal."
Platt added: "But there are different degrees of hamstring injuries - that's why we need 48 hours. It is not just, 'It's a hamstring and this is how long it will be' - we have just got to wait.
"There will be a lot of swelling and a bit of bleeding in there. We don't know how it is going to settle down. It's a blow but unfortunately, when you have got so many games in a short space of time, you are running the risk with everybody."
On a more positive note, fellow forward Mario Balotelli appears to be recovering after a virus.
The Italian has missed the last four games with the condition but is now back in training.
Platt said: "The problem was he was ill, came back and trained and had a relapse with the illness so went back down again.
"It looks as though he has got past that now. He has had two or three days' training and will have another few days before the game at the weekend.
"There is every chance he will be available for selection."