The convoy was carrying Humayoon Aini, an intelligence chief in Kabul.
Aini was unharmed but three of his fellow travellers, including a tribal chief, were killed in the attack late on Friday, the Kabul police chief said.
Two other men, including a district intelligence director, were wounded.
The interior ministry said the bomb was "recently planted by unknown militants" to target government officials, labelling the attackers as the "enemies of Afghanistan" - a phrase used to describe the Taliban.
Also on Saturday, the US-led forces in the country said they had killed more than 45 Taliban members in several incidents over the past week, in an upsurge in violence.
The US-led multinational force said that more than 40 men had been killed in operations by Afghan and international forces in the south in the past week.
About 30 died in Zabul's Arghandab district on Monday when an Afghan and Canadian patrol clashed with about 60 fighters. Another 14 were killed in Uruzgan province on Thursday, the coalition said.
Also on Saturday, two policemen were killed and three others injured when their vehicle hit a landmine near Kandahar.