The fire affected some offices including the Audit, Communications and Engineering Departments.
A source at the FAAN fire service said that the incident, which occurred around 7AM, was caused by an electrical fault.
Although there were no casualties, files and other equipment belonging to the authority were completely destroyed.
The Lagos State Commissioner of Police, Fatai Owoseni and other top police officers were on ground to maintain law and order.
The incident caused heavy vehicular traffic around the airport and its environs.
As at the time of filing this report, firefighters from FAAN and the Lagos State Fire Service were still battling to put out the fire.
VIDEO: Fire Outbreak at the headquarters of Federal Airports Authority of Nigeria in Lagos pic.twitter.com/CEY0uHfTIJ
— Sahara Reporters (@SaharaReporters) April 11, 2017