"One person has died and perhaps there are several more," said an unnamed police official, Sky News reported.
Shots were fired prior to the explosions, the Belgian news agency has reported.
Hundreds more have been trapped inside the Zaventem Airport terminal.
Airport spokeswoman Anke Fransen said: "There were two blasts in the departure hall. First aid team are in place for help."
The blasts are believed to have occurred at the American Airlines check-in desk at around 8 am local time (0700 GMT).
Footage released on social media showed people running away with smoke billowing from the building. Windows were also shattered due to the shockwave.
The explosions came four days after the apprehension in Brussels of Salah Abdeslam, the main suspect behind the November Paris attacks that killed at least 130 people.
Belgian media said the airport was being evacuated and no flights were allowed. Rail transport to the facility was also halted, Press TV reported.
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