General Abdul Raziq, the provincial police chief, said the attacker detonated a bomb-laden sedan at the gate of Kandahar city's fourth district police station, killing at least one officer.
Four other people, two police and two civilians, were injured in the blast, the police chief said.
There was no claim of responsibility for the attack but similar bombings in the past have been blamed on the Taliban, which is leading a deadly insurgency to bring down the US-backed government in Kabul.
Kandahar is the birthplace of the Taliban movement. Police and government security forces, trained by the US-led NATO mission in Afghanistan, have been prime targets of insurgents.
Interior ministry spokesman Sediq Siddiqi confirmed the attack but had no further details. "So far, we have one police death," Siddiqi told AFP.
Witnesses reported "an extremely powerful explosion".
The Kandahar Media Office, run by the local government, said the suicide car bombing "completely destroyed a civilian compound."
The Taliban ruled Afghanistan from 1996 until they were toppled by the 2001 US-led invasion for refusing to renounce Al-Qaeda leader Osama bin Laden after the September 11, 2001 attacks on the United States.
Since then, remnants of the regime have orchestrated an increasingly deadly insurgency focused on suicide attacks and bombings.