The Argentine striker scored but then limped out of the champions' 3-0 win over Stoke but the City boss expects him to return in quick time.
"I don't think it is serious. It is his hamstring for sure but maybe he won't play in the FA Cup. We will try to recover him for Arsenal."
Assistant manager David Platt added: "Sergio won't play at the weekend and is probably doubtful for the trip to Arsenal but we'll know more in 48 hours.
"It's too early to make an accurate assessment but it's a blow for us because he's been playing so well. There are different degrees of hamstring injuries which is why we need to wait to assess the extent of what has happened until Thursday."
The injury to Aguero may be offset by the return of Mario Balotelli who has missed the festive period.
"Mario has been back in training the last few days so he will be an option for us. He was ill before Christmas, then recovered and started training again before falling ill once more. He has three days of training before the Watford game so could be available for the weekend," said Platt.
Both Mancini and Platt were happy with the Blues' display against a Stoke side possessing the meanest defence in the Premier League.
"We've got to continue winning games and scoring goals - we've been creating chances but not been putting them away so seven goals in two games is pleasing," Platt said.
"We probably created the same amount of chances at Sunderland but came away with nothing so we have to be pleased with a 3-0 win today."
Mancini added: "After the derby (defeat to Manchester United) we have played good games. We were really unlucky against Sunderland and did well very against Norwich with 10 men.
"We are happy because we scored three goals against the best defence in the league." City now lose Yaya and Kolo Toure - plus midfielder Abdul Razak - to the Africa Cup of Nations and Mancini admits it is a "big problem" but would not confirm if the club will delve into the transfer market.
"I don't know. We will see but it is clear we lose three important players. We will see what happens."