Glasgow Airport has been closed and all flights have been suspended after a car hit the terminal building.
The airport was evacuated following the alert
All roads around the airport have been closed following the terrorist incident, at about 1515 BST.
Operators BAA Scotland warned people not to travel to the airport "until further notice".
Edinburgh Airport was also closed to vehicles, though flights are operating as normal. Security has been stepped up at Glasgow Central railway station.
BAA Scotland spokesman Donald Morrison said that 35,000 passengers had been expected through Glasgow Airport during the course of Saturday, the first full day of the school summer holidays.
He said the airport had been closed as a result of the incident and a motorway cordon had been set up by the police.
Mr Morrison added: "Following the incident, the terminal was evacuated in line with our emergency procedures and those people still on campus are sheltering in buildings near the airport."
Glasgow Airport is the busiest of Scotland's international airports.
Passenger numbers have grown by 60% over the last decade, with approximately 8.8 million passengers a year travelling through it.
An average of 265 aircraft fly in and out of there every day, amounting to 96,939 flights every year.
More than 40 airlines fly from Glasgow to around 90 destinations.
Travellers evacuated from the airport were being looked after at nearby hotels as uncertainty over their flight plans remained.
A number of people who were stuck on aeroplanes and on the airport strip have been taken to hotels around the airport.
About 2,300 passengers were being coached from Glasgow Airport to a reception centre at the SECC, where they would be reunited with friends and family.
Prestwick Airport was operating as normal said spokesman Neil Richardson
He advised that a number of flights bound for Glasgow Airport had been diverted to Prestwick.