The 85-ton vessel carrying 12 crewmen caught fire in the sea off about 6.4 kilometers northeast of Narodo, an island in Goheung county, South Jeolla Province, at around 8:25 a.m., the Coast Guard said.
Narodo is located about 330 kilometers south of Seoul.
A 29-year-old Chinese national and a Vietnamese, aged 23, remain unaccounted for. They are believed to have jumped off the boat right after the fire broke out.
A search is under way to find them.
Another Vietnamese sailor suffered burns and was sent to a hospital.
The fire has been extinguished by the authorities. Coast Guard officials are investigating the exact cause of the blaze. (Yonhap)