Magomed Omarov died in hospital, according to state-controlled television channel Pervy Kanal on Wednesday.
Dagestan's deputy prosecutor Arsen Bulatov added that two of his bodyguards were also dead and that a third was seriously injured and was in hospital.
Omarov and his bodyguards were caught in automatic weapons fire as they were driving into Makhachkala, Bulatov said, adding that the Dagestani prosecutor's office has launched a criminal investigation.
The minister was the target of an assassination attempt in May 2003 when his car was blown up by a remote controlled mine in downtown Makhachkala. But both he and his drivers sustained only light injuries.
Dagestan is an ethnically mixed republic between war-torn Chechnya to the west and the Caspian Sea to the east. Since 1999, it has been the scene of attacks attributed to rebel groups infiltrating from Chechnya.
In a separate incident during the day, the head of local administration in Dagestan's Khasayyurt region was also the target of an assassination attempt, the ITAR-TASS news agency reported.
The official heard a powerful blast as he was driving in his armoured Mercedes, but the car's reinforcement saved his life, officials said.
Last month, four members of Russia's security forces were killed in a firefight with armed rebels.