Ten firefighting units were working to douse the fire that started around noon at the Hazrat Shahjalal International Airport.
However, he did not specify the cause of the fire.
Electricity supply to the airport has been cut off.
Employees and passengers being evacuated from the various floors have reported seeing smoke inside the building.
Departures have been suspended as people arriving for their flights were being barred from entering the airport, a security official said.
The fire at Bangladesh's main airport may hamper flights for Hajj pilgrims.
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