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.
David Platt: "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.
"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."