Eye witnesses said the fire started in the second floor NICU's Out-Born Unit, which suffered the maximum damage.
Newborn kids suffering from serious ailments are admitted to the Out-Born Unit.
Babies were shifted to other wards safely before the fire became intense, they said.
Hospital's paediatrician, Dr Hemant Jain, said there was no information about any child getting injured.
Forty-seven newborn babies in the NICU were shifted to other ICUs, he said.
"When we entered NICU, fire was at its peak and it was difficult to breathe because of thick smoke," said sub-inspector S N Sharma of the city fire department.
Prima facie electrical fault in some equipment seemed to be the cause of the fire, he added.