Aguero was in Amsterdam on Thursday attending a concert by Colombian singer Maluma when the taxi he was traveling in collided with a pole.
Manchester City manager Pep Guardiola told reporters that his initial impressions were that the striker had broken a rib.
"Aguero has had an accident in Amsterdam and he will be back after that," said the former Barcelona and Bayern Munich boss.
Guardiola said he had not yet spoken to the player, adding: "I have been preparing training. I will speak to him today. First impression is he has broken his rib."
It was widely reported Friday that Aguero, who played in City's 2-0 win over Shakhtar Donetsk on Tuesday, could be out of action for up to two months.
The news comes as a blow to Pep Guardiola's City, who sit top of the Premier League table after six matches of the season -- ahead of neighbors Manchester United on goal difference.
Aguero has been a key part of City's impressive start to the campaign, scoring six goals as he closes in on becoming the club's all-time leading goalscorer.
A two-month absence would mean Aguero would miss not only Saturday's meeting with Chelsea, but also matches against Arsenal and a Champions League tie with Napoli.
It would also impact Aguero's participation in Argentina's faltering World Cup qualifying campaign.
Back in his homeland, Aguero's first club Independiente offered their support to the 29-year-old via Twitter.
"Strength and prompt recovery. Everyone @ Independiente is with you in this difficult moment," read the tweet.
Aguero had posted a picture of himself with Mavuma on Instagram before the accident.