A spokesman for the airport said five departure flights and five arrivals were cancelled as a result of the gale force winds.
A Met Office yellow "be aware" warning for wind has been in place since 3am for the west of the country, with gusts of about 80mph expected.
The weather warning is due to stay in force until midnight.
The airport's spokesman said the wind has died down this afternoon, but advice to passengers is to continue to check the status of their flight with their airline.
The cancelled flights come as the airport revealed yesterday it is expecting to welcome more than 160,000 passengers this weekend for the October holidays.
The October school break is one of the busiest weekends of the year for the airport.
Parts of southern Scotland are set for more dismal weather throughout the rest of today and tomorrow, with persistent heavy rain forecast.