No NATO troops were hurt as their convoy had just passed when the bomber detonated his explosives, police said.
There was no claim of responsibility, but the Taliban have vowed to step up their war to expel foreign troops and bring down the Western-backed government. Intermittent fighting has been picking up recently after a traditional winter lull.
"It was a suicide car attack on NATO. It killed eight civilians but caused no casualties among NATO because the convoy had passed when it happened," Kandahar police chief Sayed Aqa Saqib told Reuters.
Twenty people, including two policemen, were wounded, he said.
Despite the presence of about 60,000 foreign soldiers led by NATO and the U.S. military, as well as some 140,000 Afghan troops, Taliban militants have made a comeback in the past two years and more than 11,000 people have been killed in violence.