The attack occurred when the officer in the economic crimes department and his children, born in 1995 and 2000, were on the way to their house.
"All three received gunshot wounds and were hospitalized," the spokesman said.
The incident took place in the village of Gedzhuh in the Derbent district. A search for the attackers is underway.
Attacks on police have recently increased following the assassination of the republic's interior minister, Lt. Gen. Adilgerei Magomedtagirov, in the capital on June 5.