Firefighters extinguished the fire at the hospital in the eastern city of Constanta at around 0755 GMT, having brought in additional teams from nearby counties, Reuters reported.
Video footage showed patients jumping out of windows from the hospital's lower levels and firefighters carrying people out.
Interim Health Minister Cseke Attila said 113 patients were in the hospital at the time of the fire, including 10 in the intensive care unit.
Emergency response teams have installed a mobile triage unit near the hospital and 50 patients have so far been evacuated and transferred to other hospitals.
There were more than 12,100 COVID-19 patients, including 315 children, being treated in Romanian hospitals as of Thursday, including 1,364 in intensive care units.
The number of new COVID-19 infections in Romania reached 12,032 on Thursday, a new record high, and intensive care units across the country were running out of space. Romania has the second-lowest vaccination rate in the 27-nation European Union.
RHM/PR