Interior Minister Jan Jambon announced that Belgium's terror threat had been raised to its highest level, as witnesses told Belga news agency there had been shots and shouts in Arabic at the airport before the blasts hit the departure hall.
Federal police told Belga news agency that they could confirm one dead, amid chaotic scenes at the airport on the northwest outskirts of Brussels.
"There have been two explosions at the airport. Building is being evacuated. Don't come to the airport area," the airport said on Twitter.
Images on social media showed collapsed floor tiles littering the floor of the terminal hall.
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The airport has been shut down until further notice, Eurocontrol, the European organisation for air navigation safety, confirmed on its website.
Public broadcaster RTBF said regional authorities had gone into emergency mode.
Police told Belga news agency that at least one person had been killed and several others wounded.
RTBF said the blasts at the airport on the northwest outskirts of Brussels hit shortly after 8:00 am (0700 GMT).
There was no immediate confirmation of the cause of the blasts.
Europe's main stock markets retreated as the news broke, with London's benchmark FTSE 100 index dropping 0.6 per cent compared with Monday's close and Frankfurt's DAX 30 shedding 1.1 per cent.
Mike van Dulken, head of research at Accendo Markets, said that the "explosion at Brussels airport... Has knocked sentiment".