The nine respondents include the owner of the clinic, Patuakhali civil surgeon and head of gynaecology at the Barisal Sher-e-Bangla Medical College Hospital.
They will have to appear before the court on Aug 1.
Justice Salma Masud Chowdhury and Justice AKM Zahirul Hoque issued the rule on Sunday asking why those behind the botched delivery should not be prosecuted.
Secretary to the Health Services Division and director general to the Directorate General of Health Services and seven others will also have to respond within four weeks.
In March, one Maksuda Begum, 25, got admitted to Bauphul Niramoy Clinic where she gave birth to a girl via caesarean section.
A month later, she was taken to the Barisal Sher-e-Bangla Medical College Hospital with fever and seizures. Maksuda was not able to eat anything at that time.
However, an ultrasonography conducted at the hospital could not yield anything.
She got admitted to the hospital following a suggestion from a Patuakhali-based doctor. She underwent another surgery on Jul 12 when the piece of gauze was found inside her stomach.
The High Court passed the order taking the Prothom Alo report into account.
Negligence of doctors can be life-threatening for the patient, said advocate Md Shahid Ullah who brought the report to the court’s attention.