Vladimir Markin, a spokesman for the state investigation committee, said the incident occurred at 8:10 p.m. Moscow time (17:10 GMT) on Saturday on the Rostov-Baku highway, near the village of Yandare.
After police stopped and inspected a car, "shots were fired from the vehicle as it departed, and police officers returned fire. One policeman died on site, and the person in the car was wounded and taken to hospital."
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.