Tuesday's explosion also injured three other people, said regional Interior Ministry spokeswoman Marina Rasulova.
The dead officer and three wounded were all in the car when the blast occurred, she said.
But a duty officer at the Emergency Situations Ministry headquarters for southern Russia, Sergei Petrov, gave a conflicting account.
He said the car was empty and that one person was killed and another wounded - both pedestrians - in the blast.
The blast could be heard in the centre of Makhachkala, the regional capital.
Dagestan borders Chechnya and is plagued by violence, some of it linked to the war between Russian forces and Chechen rebels.