Police say the Chevy Impala was going the wrong way on Chester Street when it collided with a Nissan Altima at Sutter Avenue in Brownsville just before 1 a.m.
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The force of impact flipped the Impala, which then caught fire. But by the time police and firefighters arrived, the occupants had fled the scene.
Up to four people were in the Altima when it was struck on the passenger's side.
A 27-year-old man is in critical condition, while the rest have less serious injuries.
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The cars came to rest in front of P.S./I.S. 323, where parked vehicles were also struck in the crash.
It all happened hours before students returned to class for the first day of school in New York City.
Investigators later determined that the driver of the Impala was fleeing a previous crash, in which it had struck two cars parked in front of 1470 East New York Avenue.
"This block doesn't have speed bumps, and a lot of drivers tend to pass through here doing exorbitant speeds without any consideration that they're children in a school," neighbor Louis Burns said.
So far, no one involved in the crash has been identified.
"It's unfortunate, because even on that corner on there, I think we need a speed bump over there," neighbor Anthony Mark said. "Because things always happen in this area."
Authorities were looking for the occupants of the Impala, and the crash remains under investigation.
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