Bhushan Katta and a woman nurse who were on duty at the Neonatal Intensive Care Unit (NICU) of Punjabrao Deshmukh Medical College Hospital were booked on the charge of negligent act not amounting to culpable homicide.
Katta was arrested this morning, police said.
The medical college and the hospital are run by Shri Shivaji Education Society.
Four premature babies, born last week and kept in incubators in the NICU of the hospital, died in the early hours yesterday.
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Based on the report, a case was registered, he added.
"The bodies were handed over to parents after autopsies. We are waiting for autopsy reports to ascertain the cause of deaths," Deputy Commissioner of Police Shashikant Satav told PTI.
The nurse told the investigators that she gave wrong injections to the babies, another police official said.
Following the deaths, parents of the babies accused the doctors of negligence. Some activists of Maharashtra Navnirman Sena also allegedly thrashed Katta yesterday.
A doctor has to be present all the time in NICU which was not ensured in this case, he added.
Local MLA Ravi Rana demanded a compensation of Rs 25 lakh for the kin of each victim.
Divisional commissioner J P Guta told PTI that he would submit a report to the state government about the alleged irregularities and lapses by the hospital management.