Zalmai Ayobi, a spokesman for the governor, said: "There was a suicide car bomb attack against one vehicle of a private security company of a construction company in Kandahar city."
"Two civilians were killed and six were wounded," he said.
A witness said that one of the dead was a boy on his way to school and the other was an adult male.
Ayobi said the attack was against a convoy of Afghan guards from a security company but the targeted vehicle appeared to have driven off.
A second suicide bomber on Thursday struck the small centre of Khash Rod in the southwestern province of Nimroz and killed two more people, provincial governor Ghulam Dastagir Azad said.
The attacker had been on foot and blew up near a police vehicle in front of a mosque, he said.
"One policeman and a civilian who was going to mosque were killed. Seven other civilians who were going to mosque were injured and two of them are in serious condition," he said.
There was no immediate claim of responsibility.