The fire broke out at around 2 AM due to a short circuit in the air-conditioner in the ward where 22 children, mostly infants were admitted, the hospital's Superintendent Dr Satish Kachchawa said.
The ward was evacuated immediately, but four of the infants received burn injuries, he said.
"All the minor patients were shifted to three places - main ICU of PBM hospital and two other hospitals. Four infants received minor burn injuries and their condition is now stable," he said.
The fire had been extinguished, police said, adding Some medical equipment was damaged in the fire.
After the incident, District Collector Arti Dogra and other senior officials rushed to the hospital.
The collector has ordered an inquiry and set up a 3-member committee to probe the incident.
Rajasthan MoS for Home Virendra Beniwal also visited the patients at the hospital.