More than 80 others were hurt in the fire, which comes just weeks before thousands of athletes and foreign visitors are expected in the country for the Winter Olympics.
Videos posted on social media showed a patient hanging on to a rope dangling from a helicopter above the hospital in Miryang, in the far south, and another crawling out of a window to climb down a ladder.
The six-storey structure housed a nursing home as well as the hospital.
The death toll rose rapidly throughout the morning, as those initially pulled from the blaze succumbed to their injuries.
By lunchtime, it had hit 41, according to the presidential Blue House.
"Two nurses said they had seen fire suddenly erupting in the emergency room," said fire chief Choi Man-Woo.
All the patients had been brought out, he said, adding that evacuating 15 sick people from the intensive care unit on the third floor took longer as firefighters had to wait for medical staff to supervise the process.
All those who died were in the hospital, he said.
"Many victims were from the first and second floors of the hospital... some died on their way to another hospital," he said.
Video footage and pictures showed the building engulfed by thick, dark smoke and surrounded by multiple fire trucks.
Around 200 people were in the Sejong Hospital when the fire erupted, police said.
Jang Yeong-Jae, a surviving patient, said he was on the second floor when nurses screamed "Fire!" in the hallway and urged people to leave through the emergency exits.
"But when I opened the exit door, the whole stairway was filled with dark smoke and I couldn't see a thing," he told Seoul's major daily JoongAng Ilbo.
"Everybody was running around in panic, falling over and screaming as smoke filled the rooms," he was quoted as saying. Jang tore open window screens and escaped on a ladder erected by firefighters.
"There were so many aged patients on other floors... I wonder if they escaped safely," JoongAng quoted Jang's wife as saying.
South Korean President Moon Jae-In called an emergency meeting with advisers, and demanded an immediate probe into the cause of the blaze.
The fire came only a month after 29 people were killed in an inferno at a fitness club in the South Korean city of Jecheon -- a disaster blamed on insufficient emergency exits, flammable finishing materials and illegally parked cars blocking access to emergency vehicles.
Friday's accident is South Korea's worst fire disaster since 2003, when an arson attack on a subway station in the southeastern city of Daegu killed 192 people.
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