China's decision to relocate the oil rig in the disputed waters came after Vietnam accused a Chinese ship of ramming and sinking one of its fishing boats.
The rig had moved to a new location, Chinese Foreign Ministry spokesman Qin Gang said.
Qin said China Oilfield Services Limited (COSL) had completed the first phase of oil drilling and exploration off the controversial islands and has moved to another site for its second phase of work.
It is not clear whether Beijing's move would help bring down tensions with Vietnam.
But Vietnamese state media said the Chinese rig was still within what Hanoi considered its territory.
Qin also refuted Vietnam's charge that its boat was sunk by the Chinese vessel.
"The Vietnamese fishing boat forcefully intruded into the caution area of China 981 drilling rig and rammed into the left side of the Chinese boat and capsized," he said.
The 10 crew members on board the Vietnamese boat have been rescued, he said.
"Some countries fantasise that (China) will sit idly by while its interests and sovereignty are damaged," he added.
China urged Vietnam to "immediately stop the disturbance and damaging behaviour".
Earlier the president of the Fisheries Association in Vietnam's central port city of Da Nang, Tran Van Linh, said: "I call this an act of attempted murder because the Chinese sank a Vietnamese fishing boat and then ran away."
"We vehemently protest this perverse, brutal and inhumane action by the Chinese side," the Hong Kong-based South China Morning Post quoted him as saying.
The naval vessels of the two countries rammed into each other hundreds of times as Vietnam demanded China to move the rig out of the location.
The fracas resulted in anti-China riots in which two Chinese were killed and over 100 injured and over 460 factories, mostly set up with Chinese investments, were destroyed. China evacuated over 7,000 of its workers from Vietnam.
