The soldier, whose nationality has not been released, was attacked by a civilian when a coalition convoy was held at a police checkpoint on the road from the airport into the centre of Afghan capital.
"A young man stabbed the foreigner in his neck," Nisar Ahmad, a district police officer on duty, told AFP.
"He was rushed to hospital and the attacker ran away."
NATO's International Security Assistance Force (ISAF) issued a statement saying that "a service member died of wounds as a result of an attack in eastern Afghanistan today."
An official from the Kabul police investigation department said the NATO convoy of fuel tankers was held at the checkpoint.
"While the police were checking their documents, a young man attacked one of the foreigners and stabbed him," he said.
NATO soldiers are rarely seen on foot in Kabul, but their heavily-protected vehicle convoys have often been targeted by suicide bombers.
About 44,000 US-led NATO troops remain in Afghanistan, down from a peak of 150,000 in 2012.
All combat forces will withdraw before the NATO mission finishes at the end of this year. About 10,000 US troops are likely to stay on in 2015 for a training and counter-terrorism mission.
No NATO soldiers were hurt, but four civilians were killed and 35 wounded.
