Officers were sent to the scene just after 06:00 following concern over an item in a passenger's bag.
Large queues have built up around the check-in desks and some passengers were left standing in the car park.
A spokesperson for the airport said the central search area and domestic arrivals area were shut but the check-in desks were open. They added that passengers arriving at the airport for departing flights will face delays while checks are carried out.Police Scotland later said the terminal building had been closed as a precaution but not evacuated.
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