The gunmen shot at the vehicle, killing the officer and injuring his passenger.
In a separate development, three civilians were also injured in an attack in Ingushetia on Monday, local investigators said.
A group of civilians was fired at from a VAZ-2114 car in the town of Ordzhonikidzevskaya, in the republic's Sunzha District. Two of the three injured people are in a critical condition.
Ingushetia has seen a rise in violence in recent months. The Russia-based human rights group, the Moscow Helsinki Group, said in late September that the republic was on the verge of civil war as fighting between militants and authorities intensified. It also accused federal authorities of torture and abductions.