The Argentine, 29, was reported to be in a taxi on his way to the airport after watching singer Maluma perform.
City said he “was in Holland on his day off and has sustained injuries”.
Aguero is expected back in Manchester on Friday and will be examined by City’s medical team before the Premier League trip to Chelsea on Saturday.
Police in Amsterdam confirmed to the BBC that two people were in a taxi which crashed in the De Boelelaan area of the city.
Earlier in the evening, the Argentina forward posted a photo of himself and Maluma on Instagram with the message, “thanks for the invitation”.
Aguero’s former club Independiente sent the player their best wishes on Twitter, saying: “Strength and speedy recovery @aguerosergiokun! All @Independiente is with you at this difficult time.”
The striker has scored seven goals in eight matches for City this season, helping Pep Guardiola’s side reach the top of the Premier League and win their first two Champions League group matches.
The international break follows City’s match against Chelsea. Aguero was named in Argentina’s squad for their final two World Cup qualifiers against Peru (5 October) and Ecuador (10 October).
Argentina are fifth in the South American section standings, which only guarantees a play-off place.
BBC Sport’s Simon Stone on BBC Radio 5 live
Aguero has been in fine form this season and is one away from equalling Eric Brooks’ club record of 177 goals for City. His absence would be a major blow, particularly after it was confirmed on Thursday that defender Benjamin Mendy has ruptured the anterior cruciate ligament in his right knee.
There will be a major question mark over what Aguero was doing in the Netherlands given City have a very important game against Chelsea on Saturday. Pep Guardiola has a news conference later on Friday (13:30 BST), so we might find out more then.