The fire broke out at the Special NewBorn Care Unit of the hospital, about 900km from Mumbai, around 2:00am.
All the victims were infants between a month and three months' old, Indian officials said.
Meanwhile, Indian Prime Minister Narendra Modi has issued a condolence message over the death of the infants.
“Heart-wrenching tragedy in Bhandara, Maharashtra, where we have lost precious young lives. My thoughts are with all the bereaved families. I hope the injured recover as early as possible,” Modi tweeted.