Confirming the incident in a radio interview with Accra based Starr FM, the Somanya District Police Commander, ASP Mr Isaac Otsin said the brothers were playing with the single barrel gun, which belonged to their 70-year-old grandfather.
He said the gun was mistakenly triggered and fired into the head of the 4-year-old, who died on the spot.
Tenants in the house, who heard the gunshot rushed to the room to find the deceased in a pool of blood.
The police have deposited the body at the Atua Government Hospital morgue.
Meanwhile, investigations have commenced into the incident and statements have been taken from the parents and the grandfather, who owns the unlicensed gun.
The suspect is in police custody.