The suicide attack killed five people and wounded 33 others, including at least four children, said Hashmat Stanikzai, Kabul's police chief.
An explosive-laden car was detonated as a foreign embassy convoy was passing by in the 9th District police zone, said interior ministry spokesman Sediq Sediqi.
The British Foreign Office told CNN that it was "aware of an attack on a British embassy vehicle. We are now working with the Afghan authorities to establish more details."
The Taliban have claimed responsibility for the attack.
Pictures from Mustafa Deveci, a witness at the scene, showed at least five vehicles damaged at the scene with their windows blown out.
