Adilgerei Magomedtagirov emerged unhurt from the attack on his car as he was traveling a highway connecting the North Caucasus republic's capital Makhachkala and Buinaksk, another regional center, police said. Two of his bodyguards were wounded.
"Unidentified assailants opened fire at the motorcade of Interior Minister Adilgerei Magomedtagirov as it was heading for Buinaksk," a police source said.
Russian television channel Vesti reported that armored personnel carriers and a helicopter had been brought into the area to hunt down a group of militants thought to be responsible for the attack.
Earlier on Tuesday, Bitar Bitarov, the Buinaksk prosecutor, was seriously wounded when an explosive device planted on a roadside detonated as his car was passing.
"The car of city prosecutor Bitar Bitarov has been blown up," a police official said. "He has been hospitalized in a serious condition."
Daghestan, which borders on Chechnya, has had a troubled history in the last few years and Bitarov is the chief legal officer in a town which itself saw a horrific apartment-block bombing in 1999 that killed 64 people.