The fire broke out in one room of the intensive care unit at the Piatra Neamt county hospital and spread to an adjoining room. It was unclear what triggered it, officials said.
Seven people were injured and in a critical condition, including the doctor on call, they said.
Prosecutors said they would open an investigation to determine the cause of the fire, the country's most deadly since 2015, when a night club in the capital Bucharest burned down and 65 people died.
That blaze triggered mass protests across Romania at the country's culture of graft and lack of accountability.
Romania, which has one of the European Union's least developed healthcare infrastructures, has reported 353,185 coronavirus cases and 8,813 deaths.
Just under 13,000 people with COVID-19 were hospitalized across Romania on Saturday, including 1,172 in intensive care units.