Other officials could not be reached to confirm the details or death toll.
A police officer who would not give his name also said it was a suicide attack.
He said six police had been wounded, including a senior officer.
"It was a suicide attack and, including the border police commander of Spin Boldak, I have seen six border police wounded," he said.
A civilian worker who came out of the complex soon after the explosions said the blasts appeared to have come from a police vehicle parked inside the compound.
"There was a small explosion followed by a big one in a white car parked near the criminal investigation department inside the police headquarters," he said on condition of anonymity.
Police immediately sealed off the area and seven to eight ambulances were seen leaving the compound in the city centre.
The Taliban movement claimed responsibility for the attack, and has been behind a recent wave of suicide attacks in Afghanistan.
In mid-June, the Taliban used suicide bombers to blow open Kandahar jail, allowing more than 1,000 prisoners to escape.
The Kandahar area was where the Taliban rose to power in the 1990s, before taking over government in 1996.
US-led forces removed the movement in 2001 after the September 11, 2001 attacks on the United States.