The attack happened during the morning rush hour on Sunday not far from the office of Kandahar's governor in the heart of the city.
Sunday is a working day in Afghanistan.
"The attack happened just after the convoy passed," Kandahar city police chief Muhammad Hakim said near the scene.
"There were no casualties among the troops and only one window of a vehicle in the convoy was broken," he said.
Hakim said there were no deaths in the blast apart from the attacker.
One person was wounded, he said, referring to a passerby who had part of his leg blown off.
US-led forces were seen blocking off the site of the attack.
"The attack happened just after the convoy passed"
Kandahar city police chief
The United States leads a force of about 20,000 in Afghanistan.
The nationality of the troops attacked on Sunday was not immediately known, but most members of the force are American.
US military officials were not immediately available for comment.
Increase in fighting
Kandahar was the main stronghold of the Taliban who were forced from power in late 2001 after a US-led invasion, and has been the scene of raids and several attacks against US-led forces recently.
Nine policemen were killed in Helmand province, also in the south, on Friday.
More than 1100 people have been killed in violence in Afghanistan this year, including nearly 60 US soldiers.
US and Afghan opposition troops forced the Taliban from power in late 2001 after refusing to meet US demands to hand over Osama bin Laden.
Taliban fighters and those allied to them have been fighting against the US-backed government, US and other foreign forces since then.