The cargo ship fled the scene as the 138-tonne Chinese boat sank in the open sea, some 160 kilometres (100 miles) off the resort island.
"Ten people are missing and three others were rescued," a Jeju coast guard spokesman told AFP.
Three South Korean rescue boats and two Chinese rescue boats were searching the area, backed by six Chinese fishing boats, he said.
The collision took place yesterday as the Chinese fishing boat was anchoring because of rough seas.