A police official inside the headquarters said the blast was caused by a suicide bomber on a motorcycle.
Qari Mohammad Yousuf, a Taliban spokesman, claimed responsibility on behalf of the group in a telephone call to Reuters.
An interior ministry spokesman said: "Thirteen people were killed and 13 wounded. Seven of the dead are police." Some of the wounded were in a critical condition, officials said.
A resident of the city said the blast went off in a car park in front of the building. He said he saw casualties being taken away when he arrived at the scene.
Afghan security forces have arrested Aljazeera's correspondent, beaten the cameraman and seized his camera.
Dozens of people have been killed in a wave of attacks, including 14 suicide blasts, across southern and eastern Afghanistan in recent months.
A Canadian diplomat was among three people killed in a bomb attack in Kandahar on 15 January.
The next day, a suicide bomber on a motorcycle drove into a crowd in the border town of Spin Boldak, also in Kandahar province, and killed 23 people.
The US-backed government blames the Taliban and al-Qaida fighters who are working to expel US and other foreign forces from the country.
The surge in violence comes as Nato prepares to expand its Afghan peacekeeping force into the south of the country. The 9000-strong force now operates in the relatively secure north and west, as well as in the capital, Kabul.
The US heads a separate international force of about 21,000, made up mostly of US soldiers, fighting insurgents and hunting their leaders in the south and east.
The US is hoping to cut up to 3000 troops as Nato peacekeepers take more responsibilities in the south.