It originated from Air India's office on the second floor of the main building around 1:30pm on Friday, said Abdul Mannan, senior officer at Kurmitola Fire Station.
Ten firefighting units doused the fire around 3pm, he said.
Electricity supply to the airport has resumed, said Rasheda Sultana, the airport's chief security officer.
Aircraft have resumed departure and passengers are no longer being stopped from entering the building, she said. Arrivals continued despite the firefighting efforts.
Tajul Islam, an Air India official, said the fire gutted their entire office.
“The lockers, papers and money have been burnt. A Qatar Airways room next to ours has also suffered damage,” he added.
The building's second floor also houses the offices of Saudia, a duty officer of the Armed Police Battalion told bdnews24.com.
The authorities have not yet commented on the extent of damage caused by the fire and how it had originated.
No casualties were reported, Kurmitola Fire Station official Shafiqul Islam said.
Employees and passengers, evacuated from the various floors, reported seeing smoke inside the building.
The display screen of the airport's auto fire detector showed the text - "Fire on Air India floor" - as soon as the fire alarm went off around 1:30pm, said an airline employee.
Five more flights of Thai Airways, China Eastern, Hong Kong Airlines, Maldivian Airlines and Turkish Airlines were scheduled to leave the airport by 4:30pm. But none of them left by the time.
A China Eastern official said the airline had a flight to Kunming at 2:35pm but it was delayed due to power cut.
“The situation is same for all airlines. We hope the situation will normalise by the evening,” China Eastern Station Supervisor Abu Hanif told bdnews24.com.
Some domestic flights were also delayed.
The airport’s Director Kazi Iqbal Karim could not be reached for comments.