He also said two police officers and two other civilians were also injured in the attack.
A reporter for the AFP news agency, described the scene as one of carnage. The reporter added women could be heard screaming inside the residential compound.
Police immediately sealed off the area in the centre of the city.
Kandahar, which is the second largest city in Afghanistan, was the country's capital during Taliban rule from 1996-2001.
In a separate attack on Thursday, an explosion inside an Afghan army base near Kabul's airport killed one Nato troop and one Afghan soldier, officials said.
Several foreign troops and three Afghan soldiers were also wounded in the blast.
The Afghan defence ministry and Nato said they have launched an investigation into the cause of the blast.
Taliban leaders claimed to have carried out the attack by infiltrating the military base.