However, Najib Nekzad, a press officer for the interior ministry, said no attacker's body was found, leading police to believe the bomb was detonated remotely.
Nekzad said a rocket was fired towards the police station moments before the car exploded, killing at least five civilians and wounding five others.
Zabihullah Mujahed, a Taliban spokesman, said his group had carried out the car bombing, which he said was aimed at the Kabul police headquarters.
The Taliban uses suicide raids and roadside bomb attacks as part of its fight against the US-backed Afghan government and foreign troops.
In early December, Taliban bombers attacked twice around the time of a visit by Robert Gates, the US defence secretary.
A bomber slammed his car into a bus filled with Afghan soldiers in Kabul on December 5, killing 13 people.
On December 4, a Nato convoy was hit by a similar attack close to the capital's international airport. There were no casualties among Nato forces, but 22 Afghans were wounded, according to Nato.
The deadliest suicide attack in Kabul hit an army bus in September and killed 28 army personnel.
More than 10,000 people have been killed in the past two years, the bloodiest period since US-led forces overthrew the Taliban government in 2001.
An increasing number of Afghans are frustrated with the lack of progress toward peace.