The car bomb exploded on Sunday on a main road about 100 metres from a multinational force military base used to train Afghan security forces, the interior ministry said, adding that two people were also wounded.
"Today at 11:20am (0550 GMT) a [Toyota] Corolla taxi driven by a suicide bomber exploded ... near Camp Phoenix," the interior ministry spokesman, Yousuf Stanizai, said.
"As a result the bomber himself, a driver of a truck nearby and a civilian passer-by were killed."
The blast was on the main road between the capital and the eastern city of Jalalabad.
Most of the other suicide car blasts that have struck the capital in recent months have been on the same road and targeted at Afghan and foreign security forces.
One of the dead men was a truck driver who had parked his vehicle and was crossing the road to buy ice, said his weeping brother, who had remained in the truck.
Another witness named Atiqullah, who was slightly wounded, said he had seen a man who ran a tyre-repair shop on the side of the road being rushed to hospital with severe injuries.
It was not immediately clear what the blast bomb had been aimed at, leading police to suspect the attacker may have detonated the explosive too soon.
Four soldiers killed
Sunday's deadly car bombing came on the heels of a battle in southern Afghanistan that left a foreign military officer and three Afghan soldiers dead, a multinational spokesperson said on Sunday.
Twenty-five Afghan soldiers and another multinational force soldier were also wounded in the clash in Spin Boldak on Saturday, Lieutenant Tamara Lawrence said.
Lawrence could not give the nationality of the multinational force soldiers, who were trainers embedded with Afghan forces.
However, the French defence ministry said on Saturday that two French special forces soldiers were killed and one wounded in the south. Some 200 French special forces soldiers are stationed in Spin Boldak, near the border with Pakistan.
France has some 200 special
force soldiers in Afghanistan
The death of the two soldiers brings to five the number of foreign nationals killed in Afghanistan since Wednesday.
A Canadian and a US soldier were killed in separate battles in the south and a US citizen training Afghan police was killed in a suicide bomb in the western city of Herat on Thursday.
Major battles have raged in the south over the past days, including one that Afghan authorities said killed more than 100 Taliban in the Panjwayi district of Kandahar and another in neighbouring Helmand province in which 60 fighters died, according to the coalition.
More than 30 Afghan troops, police and civilians have also been killed.
The recent bout of violence comes just weeks before a Nato-led force is due to move into the hostile south and take over the bulk of the coalition force operating there.
There are already more than 3,500 British soldiers in Helmand and 2,300 Canadians in Kandahar, along with more than 20,000 US troops based mostly in the south.
A Taliban commander has reportedly said the clashes show the movement is strong, but multinational forces say the uptick in fighting is because they are moving into sympathiser areas.
About 3,500 British soldiers are
stationed in Helmand at present
"We're making it very clear that we are increasing our presence in the south and we are going to increase it - the Afghan security forces, coalition and Nato force," Lawrence said.
"The enemy fighters realise we are coming and we are going to push farther and farther into those areas where they had safe havens ...
"There will be more contact, there will be more interaction with those forces."
Meanwhile, a man claiming to be Mullah Dadullah, a top Taliban field commander, told the Pakistan-based AIP news agency in an interview released on Saturday that he was leading 12,000 well-armed men against the government.
"We have control over 20 districts in Uruzgan, Helmand, Zabul and Kandahar (provinces). There are 12,000 armed Taliban who are fighting in these areas," he said.
Plenty of weapons
The group had "plenty of weapons" and had recently acquired an anti-aircraft gun, the main claiming to be Dadullah said.
"Taliban are very organised. We have 1,200 bombers with us and we will conduct more suicide attacks."
He dismissed reports that he had been arrested by Afghan authorities, who said on Friday they had captured a man who had similar features to the one-legged Dadullah.
Dadullah played a key role in the Taliban's rise from Kandahar province in the early 1990s and its capture of Kabul in 1996.