The attack occurred at the traffic police station on the outskirts of Makhachkala, the republic's capital, just as officers were lining up outside for roll call.
Shamil Guseinov, the city's police chief, said the bomber detonated his explosives at the gates to the police station after police stopped him from driving through.
All those killed were at the gates and their actions in stopping the car prevented much wider devastation, he said.
A similar bombing in a neighbouring republic in August killed 24 people and injured more than 200.
In that attack, a man succeeded in crashing a bomb-laden van through the gates of the police station in Nazran, Ingushetia.
Russia's predominantly Muslim republics in the North Caucasus have seen a sharp rise in violence in the past year, with many of the attacks targeting police and other officials.
Some describe the violence as a civil war between Kremlin-supported local governments and Islamist fighters.