The blaze broke out in the Terminal Car Park 2 and was thought to have started in a diesel car before spreading rapidly on 10 October.
The man, in his 30s, was arrested on suspicion of criminal damage.
Bedfordshire Police said the investigation had concluded and it had passed the case to the fire service.
The fire service’s investigation report is due in the summer.
Luton Airport said in November that the car park would be “fully demolished” after structural reports found it unsound and work began to dismantle it in January.
The flames spread across multiple floors of the car park and caused a partial collapse of the structure.
An estimated 30,000 travellers may have had their travel plans disrupted.
