Thousands of Afghans and foreigners have thronged the airport for days, hoping to catch a flight out after Taliban fighters captured Kabul on Aug. 15.
Twenty people have been killed in the chaos at the airport, most in shootings and stampedes, as U.S. and international forces try to evacuate citizens and vulnerable Afghans.
CNN said the clash began when a sniper outside the airport fired at Afghan guards – some 600 former government soldiers are helping U.S. forces at the airport – near its north gate.
Two NATO officials at the airport said the situation was under control after the firing.
The Taliban have deployed fighters outside the airport, where they have tried to help enforce some kind of order.
On Sunday, Taliban fighters beat back crowds at the airport a day after seven Afghans were killed in a crush at the gates as the deadline for the withdrawal of foreign troops approaches.
The administration of Biden’s predecessor, Donald Trump, struck a deal with the Taliban last year allowing the United Sates to withdraw its forces in exchange for Taliban security guarantees.