A woman named Morsheda Begum was arrested in this connection, said Farid Hossain, officer-in-charge of Joypurhat Sadar police station.
Bazlur Rashid and Zoynab Begum, hailing from Bhatukundu village at Dhamurhat upazila in Naogaon, went to Joypurhat District Modern Hospital with their daughter Tamanna for her treatment on Sunday night.
The arrestee, Morsheda convinced the couple to go to Padma Lab and Consultation Centre on Sadar Road which she said was better for the infant's medical care, the police said.
The woman took the child from her parents care saying that her older brother was the physician who was going to treat her.
She fled with the baby immediately after that.
Father of the baby filed a case with the police station in this connection that night.
The police rescued Tamanna in the morning from Al Shifa Clinic and Diagnostic Centre at Hospital intersection on the same road having been informed by the clinic authorities that Morsheda arrived at the clinic with the child.
The baby was referred to Bogra for better treatment when she was brought to Joypurhat District Modern Hospital by the police.
Pediatrician Dr Samsujjoha of the hospital said Tamanna’s condition was not good.
Tamanna’s family rushed to the hospital having her the news of her resue.
The police also detained Morsheda’s husband Emran Hossain for interrogation.