Two other civilians were wounded in the attack on Tuesday.
Colonel Sher Shah, who was in the convoy, said the bomber hit the convoy on the main road linking Kandahar with the city's airport.
No Nato soldiers were injured, he said.
A civilian driving near the convoy died in the blast, while another civilian and an Afghan soldier were wounded, Shah said, adding that the bodies of the civilian and the bomber lay on the road.
On Monday, another bomber targeting a former police chief blew himself up in a market in neighbouring Helmand province, killing 17 people and wounding 47, according to the provincial governor's spokesman.
That blast wrecked shop fronts and left body parts and blood-soaked turbans among shattered glass in the bazaar of Lashkar Gah, the capital of Helmand province.
All the 17 dead were civilians, and 15 children were among the wounded, said spokesman Ghulam Muheddin.
Nato and the United Nations said it was a suicide attack.
But Qari Yousaf Ahmadi, who claims to speak for the Taliban, said Monday's attack was conducted with a remote-controlled bomb, and that it targeted a former Lashkar Gah police chief because he had served under the pro-communist government during the Soviet occupation of the 1980s.
The target and his son were killed.
"We are very sad about the civilian casualties," Ahmadi said in a phone call from an undisclosed location.
"We only wanted to kill this former police chief."
Taliban fighters rely on civilians to provide them with shelter and sanctuary during their insurgency against foreign and Afghan troops, particularly in their former southern heartland.
Ahmadi often calls journalists to claim responsibility for attacks, although his exact ties to the Taliban leadership are unclear.
The attack was the second major bombing to kill civilians this month in southern Afghanistan, where insurgents are battling Nato-led troops and Afghan forces trying to extend the weak control of the central government.
Afghanistan is undergoing its bloodiest period of fighting since US-led troops ousted the Taliban government in late 2001 for not handing Osama bin Laden over to the US.
More than 1,600 people have died across Afghanistan in the past four months, according to an Associated Press tally of reports by US, Nato and Afghan officials.