The emergency services were alerted after an electrical fire broke out in the car at about 13:50.
The Scottish Fire and Rescue Service dispatched a crew to the scene, and a firefighter wearing breathing apparatus extinguished the flames with a hose jet.
Airport operations were not disrupted by the blaze and no-one was injured.
A police spokesman said the vehicle would be recovered in due course.
Fire crews were called out after a taxi burst into flames outside the main terminal of Glasgow airport.