There was no immediate claim of responsibility.
Zemarai Bashary, the Afghan interior ministry spokesman, said two civilians were among the injured.
The Nato-led International Security Assistance Force (Isaf) confirmed the explosion had involved some of its soldiers and a spokeswoman said some suffered minor injuries.
The 37-nation Isaf does not give the nationalities of its casualties.
The Isaf airport is near Kabul's main airport and in a busy area in the northeast of the city.
An Afghan airport official said civilian flights to and from the airport were continuing as normal.
Last week, a suicide bomb wounded three foreign troops and four Afghan civilians.
On August 15, three German security officers attached to the embassy were killed when their vehicle struck a roadside bomb.