More than a dozen civilians were wounded in the Kandahar city blast which was also near a motorcade carrying Assadullah Khalid, the provincial governor, who has been critical of the Taliban movement rooted in the area.
The bomber, driving a 4WD pick-up, detonated his explosives between two vehicles in a multinational force patrol, spokesman Major Scott Lundy said. There were no multinational force casualties.
The Canadian military said one of its soldiers had suffered minor injuries in a collision between two military vehicles as they were leaving the scene.
The interior ministry said the attacker had killed himself and three civilians, and wounded 13 other Afghans.
The blast shattered the windows of several businesses and at least one shop caught fire, witnesses said. There were body parts at the scene of the blast.
Four policemen and 18 Taliban fighters were killed on Saturday in a battle that erupted after the rebels attacked a police post in Kandahar province, Khalid, the governor, said.
Police in the province also captured two men accused of rigging up car bombs and three insurgents suspected of attacks on police posts, he said.
Meanwhile, the UK ministry of defence said on Sunday that British troops had killed five suspected Taliban fighters in southern Afghanistan.
The ministry said the deaths occurred during a "cordon and search operation" to seek evidence of Taliban activity in Helmand province.
"There have been contacts between UK forces and Taliban," a spokesman said on the civil service's customary condition of anonymity. "Five Taliban have been killed and two detained."
No British soldiers were injured, the ministry said. No other details of the operation were released.
More than 3,000 British troops are operating in former Taliban strongholds across southern Afghanistan, including Helmand, as part of a Nato-led force.
Also on Sunday, the multinational force reported that it had captured an insurgent suspected of building bombs in a cave near the Kandahar village of Gumbad, where Canadian forces have a base.
In the western province of Farah, suspected Taliban fighters kidnapped four policemen after attacking their station, Izatullah Wasifi, the provincial governor, said.
In the eastern city of Jalalabad, an Afghan soldier was killed by "the enemy" on Saturday while on patrol, security officials said.
And five people were arrested after 450kg of explosives were discovered by another patrol near the city, they said.
More than 900 people have been killed in attacks in Afghanistan since the start of the year, half of them in May.
A rise in Taliban activity in the south coincides with preparations for Nato-led peacekeepers to take control of southern provinces from multinational forces.