The blast happened inside Aino Mina, a housing complex on the northern outskirts of the city that was developed in part by Mahmood Karzai, the president's younger brother.
Kandahar government spokesman Javeed Faisal said the car bomb exploded next to a restaurant area where families were dining.
Three police were among the dead, he said, adding that an investigation is underway into how the explosives-laden vehicle slipped past the community's heavy security.
Residents have special identification badges and cars are typically searched before entering the gates.
Mahmood Karzai was one of the main investors into the project, promoted as a triumph of modernity in Kandahar, which is the spiritual birthplace of the Taliban insurgency.
Dr Samad Ahmadi said at least nine bodies had been brought to Mirwais Hospital and many of the dozens of wounded were in critical condition.
