A Belgian news agency also reported that witnesses had said they heard gunshots and shouts of Arabic at the time of the explosions fueling fears that this may have been an attack inspired by Islamic State (ISIS) terrorists.
Belgian media have said the airport explosions were a “suicide attack”.
An explosion has also taken place at Maelbeek metro station in Brussels centre near the European Union (EU) headquarters.
There are now fears of several coordinated attacks across the city and the entire metro system has been shut down.
The large explosions have taken outĀ glass windows at the entrance and much of the airport’s ceiling has collapsed.
Other explosive devices have been discovered at the airport, firefighters have told journalists at the scene.
The cause of the two blasts, which occurred at around 8am this morning at an American airline check-in desk, are unknown at this stage.
Belgian Prime Minister Charles Michel has posted on Twitter: “We are following the situation minute by minute. The absolute priority is for the victims and people who were at the airport.”
It is unknown how many are injured
The blasts occurred four days after the arrest in Brussels of Salah Abdeslam, suspected of being involved in November’s Paris massacre that left 130 people dead and more than 300 injured.
Reports are saying at least 20 people have been injured and several dead
Belgian police had been on alert for any reprisal action.
Social media showed pictures of smoke rising from the departure hall where all windows had been shattered by the blast. Passengers were seen running away down a slipway from the departure lounge.
A witness said: “I was in the check-in queue and I heard an explosion. I saw smoke, I saw people panicking and running towards the exit. There was a second explosion much closer to me.
“Everyone left the airport in panic, most people left their baggage.”
He said: “I could feel the building move. There was also dust and smoke as well…I went towards where the explosion came from and there were people coming out looking very dazed and shocked.
“The thinking here is that it is some kind of terrorist attack – that hasn’t been verified by any of the authorities here at the airport.”
Witnesses have described feeling the ground rock and seeing dust coming from the ceiling.
Brussels Airport has confirmed on Twitter that two explosions have taken place and have asked people not to come to the airport.