The men - one aged in his 50s and two in their 20s and all members of the same family - are all believed to have sustained gunshot wounds.
They have been named as Diarmuid (23) and Mark (26) O'Sullivan and their father, Tadgh (59).
It it believed a dispute may have arisen between the sons over a will and the inheritance of local farmland.
At approximately 6.30am on Monday officers were alerted to an incident at Assolas.
Throughout the morning, Garda negotiators attempted to make contact with anyone in the house.
After 1.00pm members of the Emergency Response Unit approached the house and the body of a man in his 20s was discovered with a gunshot wound in a bedroom of the house.
At approximately 1.40pm two more bodies - a man in his late 50s and another man in his 20s - were discovered in adjoining lands.
Preliminary indications suggest both bodies have gunshot wounds.
Three guns - two rifles and a shotgun - have been recovered which were all legally held.
Both locations have been declared as crime scenes and An Garda Síochána has started a full investigation into all the circumstances of the incident.
A family liaison officer has also been appointed and an incident room has been established in Kanturk.
An Garda Síochána is appealing to anyone who may have any information which may assist in the investigation to contact investigating Garda at Mallow Garda station on 022-314-50, the Garda Confidential Line at 1800-666-111 or any Garda station.