Luton Airport has announced all flights will be suspended until 3 p.m.
All passengers are being told not to travel to the airport as access is “severely restricted”.
If you are affected, the airport says to get in touch with your airline.
More than 100 firefighters, 15 fire engines and three aerial appliances were at the airport to battle the fire.
Crews from Buckinghamshire, Cambridgeshire, Hertfordshire, Northamptonshire and London Fire Brigade all helped, Bedfordshire Fire and Rescue Service said.
Bedfordshire Fire and Rescue confirmed the fire has been extinguished at 9 am this morning (Wednesday 11 October).
Fire chief Andy Hopkinson says it is thought the fire started with a diesel car, and then spread through the car park.
He said up to 1,500 vehicles could have been in the car park, which has a capacity of 1,900, at the time of the fire.
Asked if there were sprinklers in the car park, fire chief Andy Hopkinson says “not that I’m aware of”.
He says the fire service would recommend to the airport that sprinklers are fitted in any redevelopment of the car park.
He also tells gathered reporters that the car park being opened from the side would have allowed the fire to spread “horizontally” before it went up through the building.