Sky News was reporting that the hospital where one of the arrested men had been taken for treatment had also been evacuated.
Police would not confirm if there was any link between saturday's incident and two failed car bombs foiled by police in central London on Friday.
The office of Gordon Brown, Britain's new prime minister, said he was "being kept aware" of the situation.
Susie Cormack, reporting for Al Jazeera at the airport, said the two men who were arrested were believed to be the driver of the Jeep and a passenger, contradicting earlier reports that there was only one person in the vehicle.
Cormack said the car looked as if it was on fire when it hit a barrier near the main terminal.
The driver then got out of the car "took out what looked like a container of flammable liquid, doused himself in it, set himself on fire and set off to the main terminal and through to the departure hall."
Cormack said the man was unable to make it to the hall as he was accosted by airport security who tried to put the fire out.
The incident has caused chaos on a busy Saturday in what is holiday season in Scotland.
Stephen Clarkson, an eyewitness, said: "The jeep is completely on fire and it exploded not long after. It exploded at the entrance to the terminal.
|The incident has caused |
chaos for holiday-makers [AFP]
"It may have been an explosion of petrol in the tank because it was not a massive explosion."
Ian Crosby, a taxi driver outside the terminal, said: "It raced across the central reservation and went straight into the building.
"It would appear to me to have been a deliberate attack. I think this was a terrorist attack."
James Edgar, another eyewitness, said the driver fled from the car and was tackled by police.
Helen Boaden, a BBC news executive who was at the airport said a traveller tried to restrain one of the men.
Boaden said: "Then the police came over and wrestled him to the ground, the fire was burning through his clothes, and finally put him out with a fire extinguisher."
She described both men as South Asian. Glasgow is Scotland's largest airport.
The White House said on Saturday it was requesting information from British officials about the crash and that security would be bolstered outside airports.