"Passenger flights into and out of Brussels airport are suspended until Sunday 27 March included," the airport said on Twitter.
"There is much damage and we do not have access to the building as the investigation is still underway."
"Until we can assess the damage, it remains unclear when we can resume operations."
Passengers forced to leave luggage behind when fleeing the airport can now collect it from the cargo section of the airport, it added.
A huge manhunt is already under way for a third attacker at Brussels airport, a man wearing a hat seen on security footage with the other two as they pushed bomb-filled bags on trolleys through the terminal, but whose bomb did not go off.