The blaze broke out in the intensive care unit of the Piatra Neamt county hospital and quickly spread to a nearby room.
Officials said it is not yet clear what triggered the fire.
They added seven other people have been injured and are in a critical condition, including the doctor on call.
Health Minister Nelu Tataru said the injured doctor, who had severe burns on 40 percent of his body, would be transferred to a hospital in the capital Bucharest.
He added six surviving patients would be transferred to separate coronavirus hospital in the eastern Romanian city of Iasi.
Prosecutors have said they will be opening an investigation to determine the cause of the fire.
Mr Tataru said: “In future legislation, all public hospitals will be coordinated by the health ministry.” He did not elaborate on this.
Local hospitals in Romania are managed by county councils, which makes the overall supervision of the health system difficult.
The health minister said the Piatra Neamt hospital would continue to run an intensive care unit on another floor.
The fire at the hospital is Romania’s deadliest since 2015, when a blaze at a nightclub in Bucharest killed 65 people.
Romania has so far reported mor than 350,000 c coronavirus cases and 8,8313 deaths.
On Saturday, just under 13,000 people were in hospital with coronavirus throughout the country.
This includes 1,172 COVID-19 patients in intensive care units.