The Argentina striker was forced off moments after scoring the third goal from the penalty spot in the 74th minute.
City do not expect to know the extent of the injury until at least Thursday but David Platt, the first-team coach, 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.
"It is difficult to assess an injury like that, how long it is going to be," Platt said. "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."
City dominated from the outset at Etihad Stadium and although they were made to wait until the 43rd minute for Pablo Zabaleta's opener, the result was rarely in doubt.
Edin Dzeko and Aguero wrapped up the routine success after the break.
"We're happy with the result and performance," Platt said. "I think the goal just before half time was more than deserved.
"But it doesn't make the second half any easier - you've still got to go out and play, but it just settles you down a bit without the clock running against you. They have shown all season it is hard to score goals against them."
"We have just got to continue to win football matches," Platt said. "We have been producing chances in games over the last month to six weeks.
"We lamented a little bit at Sunderland the chances we produced without scoring enough goals. Fortunately we are getting our ratios up."
The match was City's last with Yaya Toure before their midfield talisman links up with Ivory Coast for the African Nations Cup along with brother Kolo and the striker Abdul Razak.
Yaya Toure's absence was keenly felt during last season's tournament but Platt said the team must cope and added: "It is irrelevant whether Yaya disappears or not. The challenge is to keep winning football matches.
"We have a squad of players that we will have to choose 11 from. Whichever 11 we put on the park we would expect to go and take the points." Stoke provided little threat during the game and their manager Tony Pulis made no excuses for their lacklustre display.
"I've no complaints, they were the better team," Pulis said.
"Someone has just asked me what the difference was - I said about £220 million [Dh1.3 billion]. For us to come here we have to bring our 'A' game and City have to be off it.
"That wasn't the case today but you have to sometimes open your eyes and look at the reality of everything. They have got a bit of a head start on clubs like us.
"I don't know whether it was because it was the fourth game in the holiday period and we didn't bring our 'A' game - but I am not going to criticise the players.
"They still worked their socks off, they worked very hard. City were the better team.
"You hold your hands up and dust yourself down."