Gunfire between Afghan security forces and unknown assailants erupted at the north gate of Kabul airport in the early hours of Monday morning, according to the German military.
One Afghan security officer was killed and three others were injured in the battle, the Bundeswehr said on Twitter.
US and German armed forces were also involved in the clashes. No other injuries have been reported.
The airport has witnessed chaotic scenes in recent days, as the US, Germany and others seek to carry out evacuation flights following the Taliban's swift takeover.