Police said the fire started in the boat's engine room about 4:30 a.m. Saturday. The 20-ton vessel was 15 miles off the shore at Gunsan, a coastal fishing village.
Police said the crew tried extinguishing the blaze themselves before calling for help, which slowed down response time.
Yonhap News Agency said 10 men were pulled from the water about 2 hours after they jumped overboard. Nine died of hypothermia.
One of the 10 survived and a search was under way for an 11th crew member, police said.