"There will be no passenger flights into and out of Brussels airport tomorrow March 24," Arnaud Feist said in a tweet today as the probe into the attacks continued.
The departure hall was completely wrecked, with part of the ceiling collapsing down as passengers waiting to check-in struggled out of the smoke-filled building in panic and fear.
Another attack shortly after on the Brussels metro system left about 20 dead, with some 250 injured in both incidents.
Those who did so could now contact their airline to get their luggage back, it said, but they would still not be able to retrieve their cars.
The resumption of cargo services, either later today or tomorrow, was being looked at, it added.