A formal complaint was lodged with the Chinese Embassy in Hanoi over the March 20 incident after a patrol boat chased the fishing boat before firing on it.
A Vietnamese Foreign Ministry spokesman said the attack was "an extremely serious incident," a report by the official Vietnamese News Agency said.
Spokesman Luong Thanh Nghi said China violated Vietnam's sovereignty over the Hoang Sa archipelago -- the Vietnamese name for the Paracels -- threatened the lives of Vietnamese fishermen and damaged their property.
"Vietnam strongly protests, urging China to investigate and seriously deal with the wrongful and inhumane act and compensate Vietnamese fishermen for their loss."
The incident is the latest clash between Vietnam and China involving the Paracels, a dispute that spilled over into a brief armed conflict between South Vietnam and China in 1974.
Prior to the conflict Vietnam and China claimed various of the unoccupied rocky islands -- known as the Xisha Islands by Beijing -- which lie about 180 nautical miles from both Vietnam and China's Hainan Island.
An attempted landing by Vietnamese soldiers on a Chinese-claimed island resulted in a 2-day battle, including warships, that left China in complete control of the more than 30 islets, sandbanks and reefs covering around 5,800 square miles of ocean.
Beijing claims sea rights over a swath of area extending south as far as the island of Borneo.
The Paracel Islands issue is one among many South China Sea disputes involving China and regional neighbors, including the Philippines and Japan.
In January, China said it will survey the disputed Diaoyu Islands to "safeguard China's marine rights," a Foreign Ministry spokesman said at the time.
The survey of the islands -- known as the Senkaku Islands by Japan which administers them -- will be part of a larger project of island and reef mapping started in 2009, spokesman Hong Lei said in a report by state-run Xinhua news agency.
"Diaoyu Island and its affiliated islets have been the inherent territory of China since ancient times," said Hong.
Beijing and Manila have been at diplomatic loggerheads over competing claims for the Scarborough Shoal, a triangular collection of reefs covering less than 60 square miles and whose highest point is around 10 feet above sea level.
The Philippines-administered shoal is more than 400 miles off the Chinese coast but 150 miles off the coast of Zambales, a province on the western shore of Luzon Island, the largest and most northern Philippines island.
Since mid 2012 Chinese patrol boats have been sailing in waters around the shoal, at times blocking entrances to passages among the islets.