The Argentinian Football Federation said Aguero fainted at half-time in Tuesday's 4-2 friendly defeat against Nigeria in the Russian city of Krasnodar, and he was taken to hospital, however City stated he was always conscious.
Aguero scored after 36 minutes in Krasnodar to put Argentina 2-0 ahead, but did not come out for the second half and was replaced by Dario Benedetto.
The Argentinian federation stated in a Twitter post: "(Aguero medical bulletin) He fainted and was therefore transferred to carry out routine checks just as a precaution."
It later added that Aguero had left hospital and was "at the hotel with the rest of the delegation". City expect Aguero back in Manchester for a medical check-up ahead of the Premier League match at Leicester on Saturday.
The Premier League club announced on their website: "Sergio Aguero has been cleared by doctors to return to Manchester as planned after suffering a dizzy spell during Argentina's 4-2 defeat by Nigeria in Krasnodar today.
"Sergio never lost consciousness, and was taken to hospital for precautionary medical checks. He will be assessed by the club's medical team ahead of this weekend's Premier League trip to Leicester City."