The attack on Kharum Dzeytov's house in the city of Nazran took place at 1:20 a.m. Moscow time on Thursday (21:20 GMT Wednesday).
"During the gunfire no one was injured," the source said. A search for the assailants has been launched, and an investigation is underway.
Earlier the same night, unidentified gunmen opened fire on the house of Isa Korigov, chief criminal investigator in another Ingush city, Malgobek. The building was slightly damaged, but no one was hurt in the attack. However, shortly afterwards an explosive device went off as a group of investigators arrived at the scene. Four people, including Korigov, were wounded and later hospitalized.