RFE/RL's Russian Service reports that at least two gunmen climbed over a fence to enter the family's property, then forced the three men into a nearby shed where they shot them dead.
Two of the victims were brothers, aged 25 and 17. The third, a 50-year-old man, has been identified in press reports as the young men's father.
A search is under way for the killers. There have been no official statements from police about possible suspects or a motive.
The killings come amid rising violence in the volatile republic, which borders Chechnya. Much of the violence is seen as targeting Russians and Russian-speakers.
On September 7, an ethnic-Russian doctor was shot and killed outside her home in the Ingush capital, Nazran.
Local officials have blamed Islamist rebels for much of the unrest in the region.
Earlier in September, some 2,500 Interior Ministry troops were sent to the region to support local security forces.