They were picked up March 3 and have been held in custody since, Pham Thi Huong of the People’s Committee of Ly Son island in Vietnam’s Quang Ngai province told AFP.
“The captain spoke to his family and told them the Chinese are demanding 70,000 yuan ($11,000) for their release,” she said, adding it was not clear whether this amount was for one or both boats.
Officials advised the family not to pay and have asked Hanoi to press for their release, she said.
The incident is the latest in a string of diplomatic skirmishes between the neighbours over islands in the South China Sea.
In late February, Vietnam claimed China had prevented 11 Vietnamese fishermen from approaching the Paracel Islands to avoid strong winds.
The Paracels — or Hoang Sa Islands in Vietnamese — have been controlled by China since 1974 but are claimed by Vietnam.
The two countries also have competing claims over the Spratly islands — a potentially oil-rich archipelago.
Taiwan, Brunei, Malaysia, and the Philippines also claim all or part of the Spratlys.