"Thirteen people, most of them police, have died in the bomb blast in Kandahar city and were taken to the Kandahar public health hospital," a doctor on duty, who gave his name as Mamoon, said.
"Eleven are wounded, most of them in critical condition," he added.
The interior ministry confirmed the blast was caused by a bomb.
"A suicide bomber wanted to get into the headquarters and while police were searching him he detonated the bomb which killed 13 people, among which seven are police and six civilians," ministry spokesman Yousuf Stanizai told AFP.
"The suicide bomber was totally blown into pieces. This is the work of the Taliban and al-Qaeda, the enemies of peace and development in Afghanistan," Mr Stanizai added.
A destroyed motorbike was at the scene of the blast, which was splattered in blood, according to an AFP journalist.
"We think the bomb was attached to a motorbike that was parked outside the building," police commander Bashir Khan said as he surveyed the site of the blast.
Police and Canadian soldiers with the US-led coalition force in Afghanistan immediately sealed off the area.
Purported Taliban spokesman Qari Yousuf Ahmadi told AFP, "It was carried out by one of our mujahedin (holy warrior) brothers. It was a suicide attack aimed at the police headquarters."
Kandahar, the birthplace of the Taliban movement that rose to control most of Afghanistan by 1996, has seen the worst of a rash of suicide and car bomb attacks that have claimed dozens of lives in past weeks.
Around 1,700 people were killed in insurgent-linked violence last year, many of them militants killed by Afghan security forces or by troops from the US-led coalition helping the government to hunt down insurgents.