Local television showed pictures of a body in US military uniform lying on the ground.
An AFP reporter at the scene saw another US soldier being treated for injuries.
'Foreign soldier killed'
Al Jazeera's Hamish MacDonald in Kabul said officials at the US embassy had confirmed that one US military officer was killed in the blast, besides the civilian casualties.
He said: "We have been told that four Afghan civilans were also killed, and four others wounded.
Zemarai Bashary, an interior ministry spokesman, said five Afghan civilians were killed and five wounded.
But Sayed Mohammad Amin Fatemi, the health minister, said that one Afghan civilian died in hospital from severe wounds and eight others were hospitalised.
A wide area around the van, which was reduced to a small chunk of metal, was covered in fragments of metal, broken trees and other debris.
The multinational force said the explosion, caused by a explosives-laden mini-van, targeted two of its armoured vehicles. Witness accounts
Those who witnessed the blast said that several people were killed at the scene, about 500m from the airport.
Mohamed Fahim, a tailor, said: "The two foreign vehicles were driving towards the airport. I didn't see the bombers' vehicle but I saw the explosion. One of the two vehicles flipped onto its side, hitting two civilian vehicles."
He said that he saw a dead body taken from each of the civilian vehicles.
Kabul has been struck by a series of suicide attacks this year.
The last was on Tuesday and had killed at least 13 people, including a mother and her two children going to school.
Four days earlier, a similar blast destroyed a military bus, killing 30 people in one of the deadliest attacks in the city in recent months.