The vehicle involved is understood to have fallen from an upper level of the car park.
Photos have shown a barrier missing on the third storey – level two – of the multi-storey building.
BBC reporter Helen Mulroy said the car appeared to be on its side on the ground and wedged against the side of the car park.
A crane was seen positioned above the vehicle, which has now been removed.
People at the scene told the BBC the car, with one man inside, appeared to turn the wrong way when exiting the car park.
It then crashed to the ground.
Terminal Car Park One is a four-minute walk from the main airport building and has options for motorists to park their vehicles themselves or use meet-and-greet services.
Passengers due to have their cars delivered to the car park by third-party services remain in a long-stay site further away from the terminal.
They have been told to collect them from there instead.