It is thought there were about 1,500 vehicles in the 1,900-capacity car park at the time of the fire.
The exact cause of the blaze and the number of vehicles damaged is not yet clear.
A temporary ramp was set up at the car park to enable undamaged vehicles to be removed.
However, Luton Airport said it was "unlikely" any vehicles would be salvageable
"Regrettably, it is unlikely that any vehicles in the car park will be salvageable but this is still in the process of being assessed," said an airport spokesman.
"We recognise this has been an extremely distressing time for all concerned and we would like to thank our customers for their ongoing patience and understanding while we work through the many complexities following this incident."
The spokesman said the airport had provided the Motor Insurers' Bureau with the registration details of 1,405 vehicles and was working with the Association of British Insurers to try to retrieve any personal items.