According to BBC News, the fire service said the first call about a fire involving a car on level three of the multi-storey had come at 20:47 BST.
Bedfordshire Fire Service said 15 engines had been sent to the airport.
"Andy Hopkinson, Bedfordshire's chief fire officer, said the service had "no intelligence than to suggest it was anything other than an accidental fire".
He said it was thought the fire started with a diesel car, and then spread through the car park. Further adding, “About 1,500 vehicles may have been in the car park and subsequently damaged."
Following the 'significant' fire, London Luton Airport on X/Twitter published a statement at 09:31 this morning which reads “Emergency services remain on the scene following last night’s fire in Terminal Car Park 2. Our priority remains supporting the emergency services and the safety of our passengers and staff. We’re working hard to get the airport operational as soon as possible. All flights are currently suspended until 3pm today (Wednesday 11th October).
Passengers are advised not to travel to the airport at this time, as access remains severely restricted.
For queries relating to a parked vehicle or future booking please contact email@example.com.
Passengers should contact their airline for information regarding their flight. Updates to follow.”
On the Bedfordshire Fire & Rescue Service website at 10am they confirmed that “The fire service have now scaled back and this is no longer a major incident.
A number of agencies have been released from the scene and we continue to work with colleagues from the airport and police. The fire service will continue to be on the scene for the rest of the day.
A total of five casualties were treated for smoke inhalation and have been discharged. They included one member of airport staff and four firefighters.
An investigation into the cause of the fire will begin once it is safe to do so.
There is still considerable congestion around the airport so please avoid the area.”