The 600-metre (1,970-foot) -long rig is being towed southeast of its current position south of Hainan Island and will be in its new location closer to Vietnam by Friday, the Maritime Safety Administration said on its website. It asked vessels in the area to give it a wide berth.
Vietnam's government isn't expected to react strongly to the placement of the second rig because it lies far to the north of the politically sensitive waters surrounding the Paracel Islands, where ships from the two countries have been ramming each other for more than 40 days near the first oil rig.
A Vietnamese Foreign Ministry official who spoke on normal condition of anonymity said Hanoi believes that no country should take unilateral action in contested waters, but that China has explored the area previously without causing a crisis in relations.
Vietnamese authorities broke up a small anti-China protest in Hanoi and detained several people Thursday, activists said, a day after high-level talks over an oil rig in disputed waters ended in deadlock.
Around a dozen activists briefly waved banners and shouted "Chinese oil rig get out of Vietnam!" and "silence is cowardice" - a dig at Hanoi's handling of the dispute - before police forced them to disperse.
Around seven activists were detained by police, according to reports posted on activist blogs. Police did not confirm the detentions.
The shifting of the rig came as officials from both sides said they made no progress in talks Wednesday over the deployment of the other Chinese rig on May 1 that sparked the current standoff. Each country claims the Paracels as its territory and accuses the other of instigating the ship rammings around the rig.
The first rig's deployment triggered anti-China demonstrations across Vietnam that led to attacks on hundreds of factories believed to employ Chinese workers, five of whom were killed and hundreds more injured. Many of the factories were built and run by investors from Taiwan, which has nothing to do with the current dispute.
China's military expelled Vietnamese troops from two of the islands in the group in 1974, and in 1988 used force to kick Vietnam out of Johnson South reef in the Spratly Islands to the east.
The border between China and Vietnam in the area of the second rig near the mouth of the Tonkin Gulf has never been properly demarcated, despite five rounds of talks on the matter.
China claims virtually all of the South China Sea, which is rich in natural resources and crisscrossed by some of the world's busiest sea lanes. That has brought it into dispute with other neighbors, including the Philippines, a US ally.