The Taliban claimed responsibility for the attack on the European Union Police Mission in Afghanistan (EUPOL), which advises Afghan law enforcement authorities.
The insurgents have launched a wave of attacks around the country since the drawdown of most foreign troops last year to a small training force.
EUPOL spokeswoman Sari Haukka-Konu confirmed that one of the mission's vehicles was hit by an explosion near Kabul airport.
She said all the EUPOL personnel "are in a safe place" with non-fatal injuries, but another person travelling in the vehicle was killed. She did not give the person's nationality.
Police spokesman Ebadullah Karimi said a suicide bomber in a Toyota Corolla rammed a foreign vehicle on the road from Kabul's main airport to a NATO military installation nearby.
