Zagir Arukhov, Dagestan's minister for ethnic policy, information and external communications, was killed by the blast, which occurred outside a building across from a police station in the regional capital, Makhachkala, police spokeswoman Marina Rasulova said.
The other victim was an unidentified woman, she said.
Rasulova had initially said two women were killed in the explosion. She had no information about injuries, but Interfax quoted an unnamed police official as saying an unspecified number of people were injured.
An ethnically mixed, mostly Muslim region on the Caspian Sea, Dagestan borders Chechnya and is plagued by violence, some of it linked to the war between Russian forces and Chechen separatists and some to local criminal activity.
For months, Dagestan has seen a series of bombings and other attacks on police and other law enforcement authorities.