The senator in question is Issa Kostoeva, and the attack occurred close to Nazran, the republic's largest city and its former capital.
No casualties have been reported.
"The incident took place in the Ekazhevo village at around 1.50 a.m. [21.50 GMT Saturday]. A group of unidentified people drove up to the senator's house and opened fire with automatic weapons and a grenade launcher," a police source said told RIA Novosti.
The assailants then fled the scene.
A search is underway for the attackers.
Ingushetia neighbors troubled Chechnya, and has seen an increasing number of attacks on the authorities by armed militants of late.