Two of the detainees are Hasina Akhter, wife of victim Md Abu Taher, and her sister Nasima Akhter.
Police recovered the throat-slit bodies of Taher, 35, a labourer, and his four-year-old daughter Bibi Fatema from their house on Saturday morning.
A blood-stained knife was recovered from the spot.
Hasina claimed that she found the bodies after returning home from work around 9am.
However, police suspected that the incident might have happened over Hasina’s ‘extramarital affairs’.
Neighbours told police that the couple locked into an altercation three days ago over a red sari the housewife wore as Taher alleged that it was given by someone else.
Hasina claimed that the sari was given by her employer after being satisfied with her work but Taher did not believe her, they added.
Police said they were looking into the incident as the victim’s wife was giving misleading information.
Assistant Commissioner of Chittagong Metropolitan Police (CMP) Md Quamrul Islam said, “Prima facie, it seemed that it’s a murder incident which took place over family feud. We’re investigating whether outsiders were involved in it.”