The country's public broadcaster VRT said there were up to 13 people dead and a further 35 wounded.
Video and images on social media showed smoke rising from an airport building and shattered windows.
Confused and shocked passengers fled the terminal to safety as they were evacuated by armed police.
Footage also showed ceiling tiles littered across the floor and strewn black luggage belts, cases and bags at a check-in desk.
According to reports the suspected terror attack centred on an American Airlines desk in a departure hall at around 8am.