The Boeing 767 bound for Miami experienced an "uncontained engine failure", officials involved in the investigation said.
The pilot aborted the take-off and evacuated everyone on board via emergency chutes as black smoke billowed from the plane.
Twenty people suffered minor injuries, the fire department said.
Nine crew members and 161 passengers were on board.
A federal official quoted by the Associated Press news agency said the plane appeared to have suffered a rare and serious type of engine failure in which parts break off and are spewed outside the engine.
Passengers reported an explosion followed by flames and black smoke as the plane was speeding down the runway.
Sarah Ahmed said everyone on the right side of the plane rushed from their seats and moved to the left side.
"People are yelling, 'Open the door! Open the door!' Everyone's screaming and jumping on top of each other to open the door," she told WLS-TV.
"Within that time, I think it was seven seconds, there was smoke in the plane and the fire is right up against the windows, and it's melting the windows."
The incident took place at 14:35 local time (19:35 GMT).
An initial statement by Federal Aviation Administration (FAA) said the plane had burst a tyre, but that information was later deleted from the statement.
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American Airlines said passengers who still wanted to travel had been put on another flight to Miami.
Elsewhere, a FedEx plane caught fire at Fort Lauderdale, Florida, airport after its landing gear collapsed on landing, the FAA said.
An American Airlines plane has caught fire on the runway of Chicago's O'Hare airport while taking off.