The incident took place in South Sunamganj Upazila on Saturday night.
The victims are, ‘Alauddin’, 71, Beauty Khanam, 30, and ‘Asifa’, 9.
Police arrested the perpetrator, Alfu Miah, after the incident.
His younger brother Shahjahan Miah said Alfu suddenly attacked the family members with an iron pipe around 11:30pm and killed them.
“He was mentally ill and often had these fit of rage,” he said.
Sunamganj Superintendent of Police Harunur Rashid and Deputy Commissioner Sheikh Rafiqul Islam visited the scene of the incident.