Emergency services were called to the scene after concerns were raised about a piece of cargo on a KLM flight arriving from Amsterdam.
A spokesman for the airport said the alarm was raised shortly after 10:00 and the aircraft had been cordoned off while investigations were carried out.
Part of the international terminal has been evacuated and closed off.
But all other areas of the airport are said to be fully operational.
Pictures from the airport showed a large number of emergency vehicles, including several fire appliances, ambulances and an environmental protection unit, close to the runway.
More about: Glasgow