The Anadolu news agency said the fire started when an oxygen cylinder exploded at the privately-run Sanko University Hospital unit in Gaziantep.
The agency cited a hospital statement identifying the victims as being aged between 56 and 85. The fire was quickly brought under control.
The statement said 14 patients undergoing intensive care treatment were transferred to other hospitals. An investigation was underway.
Intensive care units across Turkey currently have a 74% bed occupancy rate due to the coronavirus outbreak, according to government figures, although medical associations have claimed that hospitals are overrun.
On Friday evening, the Health Ministry reported 26,410 new cases over the previous 24 hours, bringing the total since March to 1.98 million. The figure includes asymptomatic cases that Ankara did not report in the four months to late November.
A record daily high of 246 COVID-19-related deaths were recorded, the ministry said, taking the total to 17,610.
