The remaining 12 fishermen were rescued after the ship went down six kilometers (four miles) off Kunashir Island, one of Russia's South Kuril Islands, at 1:00 p.m. local time (3:00 a.m. GMT), the Far East rescue service said.
The body of the dead crewmember has been recovered, and the rescued have been taken to Kunashir Island. All the fishermen are Russian citizens.
The rescue service said two Russian ships are currently searching the area for the missing fisherman.
"Border guards are assisting in the search by scanning the sea from their watchtowers on Kunashir Island," the sea rescue service on Sakhalin Island, west of Kunashir, said, adding that aviation might also be engaged.
The weather in the area is calm, but heavy rain and strong winds are expected in the evening, which could complicate the search effort, the service said.