The father of the family was rescued in critical condition and admitted to a hospital, police said.
The incident took place at Binnakandi village in Fatehpur Union of Gowainghat Upazila on Wednesday morning, said OC Abdul Ahad of Gowainghat Police Station.
The dead were identified as Alima Begum, 30, her son Mizan Ahmed, 10, and daughter Tanisha Akter, 3.
Her husband, Hifazur Rahman, 35, was admitted to Sylhet Osmani Medical College Hospital in critical condition.
Hifazur’s neighbours visited his house on Wednesday morning to wake him, said OC Abdul, citing locals. When they heard moans coming from the house they broke in and discovered the bodies. A bloody Hifazur was then rushed to the hospital.
Upon receiving the news, the police recovered the bodies and sent them to Osmani Medical College morgue for autopsy. The bodies had wounds from sharp weapons.
The police are investigating the murder, said Sylhet ASP Lutfur Rahman.