The fire sent dense black smoke billowing into the sky, the New York Times reported.
The blaze shut down one of East Africa’s most important transportation hubs, with only emergency landings permitted.
The fire started at around 5 am, when many flights to and from Europe and elsewhere are scheduled.
It was contained after several hours, Kenyan officials said, but there was no indication of when the airport would reopen.
The airport handles 16,000 passengers a day, officials said.
Many incoming flights were diverted to the Indian Ocean coastal city of Mombasa.
The fire came less than two days after problems with a fuel jet pump forced the diversion of flights to other regional airports including those of Mombasa, Entebbe International Airport in Uganda and Kigali International Airport in Rwanda.
The blaze sent a plume of black smoke that was visible from the Kenyan capital a few miles away, witnesses said.
There were no immediate reports of casualties.