Judicial Magistrate Rajib Kumar Deb passed the order when they were produced before the court, said Advocate Omar Faruk.
A group of lawyers led by Advocate Elias Arif filed a petition before the court seeking bail for them.
Those who have been granted bail are – Parvin Akhter, 55, wife of late Abul Kalam of Kusumpur union in Patiya upazila, her daughters Selina Akhter Seli, 25, Rozina Akhter, 20.
But the court rejected bail petitions of two others in the same case.
On Friday afternoon, five people including the woman, her two daughters and son, were tortured and humiliated at Paharchanda area under Harbang union of Chakaria accusing them of cow theft.
Later, they were paraded across the village with their hands and waists tied-up with rope before being taken to the office of UP Chairman Miranul Islam.
The UP chairman allegedly beat them up when they were taken to the office.
But when their physical condition deteriorated, the victims were handed over to police who took them to Chakaria Hospital for treatment.
Mahbubul Haque, a resident of Bandabonkhil village, filed a case against the five people on Friday night.
Also read: Charged with stealing, mother, children tortured in Cox’s Bazar
The accused are- Parvin, her two daughters Selina and Rozina, son Emran, 23, and Mohammad Chottu, son of Delwar Hossain of Barbakia in Pekua upazila.
The woman and her children were sent to Cox's Bazar district jail on Saturday afternoon.