Some reports suggest that it was driven by a suicide attacker.
Al Jazeera's David Chater, reporting from Kandahar, said that the explosion could be heard across the city.
"This was a massive explosion, and the whole city heard it. The blast occurred near a house owned by Hamid Karzai's [the Afghan president] brother, and Afghan MPs and local officials are among the injured," he said.
"The heart of Kandahar's political and security establishment has been attacked, and it appears that the Taliban are launching a major campaign in the area."
No group has so far claimed responsibility for the attack.
Kandahar has been the scene of a series of bomb attacks blamed on Taliban fighters.
In June, bombers blew open the Kandahar jail, enabling more than 1,000 prisoners to escape.
In September, two bombers blew themselves up inside the provincial police headquarters, killing five people and wounding nearly 40.