No one but the attacker was killed by the blast, which occurred shortly after noon, Kandahar provincial police chief Gen. Abdul Razaq said.
According to Razaq's account, a bomber believed to be 14 or 15 years old entered the station by claiming he was carrying a letter of complaint, which he told guards he was trying to deliver to police authorities.
The teenager managed to pass through checkpoints without the explosives being found, and was inside the police compound when an Afghan border policeman shouted at him, asking where he was headed. He immediately detonated the explosives.
Razaq's office was partially destroyed and the windows of his office were shattered.
The one-time Taliban stronghold of Kandahar has been particularly hard-hit by violence as insurgents seek to destabilize the local government. Three bombings in one day last week killed 13 people in the city.