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.
Airport spokeswoman Anke Fransen said: ‘There were two blasts in the departure hall.’
The attacks follow the dramatic arrest of Paris attacks suspect Salah Abdeslam in the Belgian capital on Friday – four months after November’s terror in the French capital that left 130 people dead.
Sky’s Alex Rossi had just checked-in at the aiport when he heard ‘two very, very loud explosions’.
‘I could feel the building move. There was also dust and smoke as well,’ he said.