Explosions could be heard on the airport road and other parts of Tripoli though it was not immediately clear who was fighting whom.
British Airlines canceled its flight to London, it said on its website. Turkish Airways canceled its flight to Istanbul.
Social media websites said several rockets had hit the parking area in front of the main terminal, Reuters reported.
The airport area has been controlled by militia fighters from Zintan in northwestern Libya since the overthrow of Muammar Gaddafi in 2011 though other groups have challenged them.