The fire occurred late on Friday at a hospital in Jhansi city in India's Uttar Pradesh state.
Officials said the blaze spread quickly through the ward, where 55 infants were being treated.
Forty-five babies were rescued and are receiving medical care, said Bimal Kumar Dubey, a local official.
It was not immediately clear what sparked the blaze.
Brajesh Pathak, the deputy chief minister of the state, visited the hospital and met with families on Saturday.
He pledged government support for the victims' families and promised a thorough investigation.
"We will identify those responsible for this tragedy and take strict action. The government stands with families during this difficult time," he said.
When the firefighters arrived, the ward was engulfed in flames and plumes of smoke.
Rescuers had to break through windows to reach the newborn babies.
Witnesses said the rescue operation began about 30 minutes after the fire erupted, delaying evacuation efforts.
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