The trawler Oryong 501 became stranded in the Bering Sea at around 05:20 GMT, the South Korean government said.
The 60-strong crew comprised 35 Indonesians, 13 Filipinos, 11 South Koreans and a Russian inspector.
Russian media said seven people had been saved, but weather and water conditions were hampering the search.
The boat sent no distress signal before the incident, the RIA Novosti news agency reported, citing law enforcement officials.
The South Korean news agency Yonhap said the 1,590-tonne Oryong 501 was built about 40 years ago and was operated by Sajo Industries.
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