No casualties have so far been reported and it is still not clear what caused the blaze.
Jomo Kenyatta International Airport is a regional hub for East Africa and there is likely to be much disruption to long-distance flights to other countries.
All inbound and outbound flights have already been cancelled.
All passengers have been evacuated and people urged to stay away.
There are unconfirmed reports that the fire started at the airports immigration offices.