The Korea Jeju Coast Guard found the 25-ton vessel with its upper side entirely burnt between 7 a.m. and 9 a.m. on Tuesday, Vietnam News Agency reported.
The rescue team found one Korean member of the missing crew unconscious without a life jacket in waters 7.4 kilometers south of the boat.
He was taken to a hospital on Jeju Island where doctors pronounced him dead.
The Vietnam Labor Management Board in South Korea has confirmed the boat fire information and said the youngest among the six missing Vietnamese victims is 24 and the oldest 45.
The Korea Jeju Coast Guard has also provided the names and personal identification details of the fishermen to Vietnamese authorities.