"The airport will remain closed through Wednesday," the airport's chief executive Arnaud Feist said on Zaventem airport's official twitter feed.
In a briefing, Feist added: "It's too soon to evaluate the damage in the terminal. We don't yet have access since the investigators are still busy with their probe."
"Tomorrow (Wednesday) we'll see the state of the terminal and whether we can quickly fix what was damaged and restart some of the facilities," he said.
Under normal circumstances about 20,000 people work at the airport daily, he said.
"But we don't systematically control people entering the airport and we don't check their luggage either," Feist said.
All flights into Brussels were being diverted to other Belgian airports or in some cases to neighbouring countries.