Six others are in critical condition after the fire at Hyosarang Hospital, about 200 milles south of Seoul.
Most of those who died are thought to have been in their 70s and 80s, and confined to their beds.
Officials said most of the people who died suffocated because of toxic fumes. The fire was put out within half an hour.
Police said they had detained an 81-year-old patient suffering from dementia after security video footage showed him entering an area where the fire began, reports said.
The fire broke out shortly after midnight at a three-storey annex.
Agencies report that many patients on an upper floor of the building were unable to evacuate as their rooms were filled with smoke from the fire.
The nurse who died had been trying to douse the flames with a fire extinguisher, according to AFP.
Police said the building had recently undergone safety checks, reported Yonhap news agency.
Hospice director Lee Hyung-seok, apologized and told reporters: “I’ve committed a grave sin… There is no excuse when valuable lives were sacrificed.”
The incident comes at a time of mourning for South Korea after more than 300 people died in a ferry sinking last month.
The hospital incident also comes a day after seven people were killed and 20 others injured in a fire at a bus terminal in Goyang city.
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