The protest started in the Vietnam-Singapore Industrial Park 1 (VSIP1) in the southern province of Binh Duong, and followed demonstrations by thousands of Vietnamese across the country over the weekend.
"It is now spreading to VSIP2," Nguyen Van Leo, head of the labour department in the industrial park said. "At least 3,000 workers are still protesting in VSIP2."
"We are worried that the protest may get out of control and violent actions of workers could destroy assets," a police official told dpa on condition of anonymity.
It is thought to be the biggest demonstration in the authoritarian state in many years.
Local media showed photographs of flag-waving crowds carrying banners reading "China, get out of the East Sea (the South China Sea)" and "Long live Vietnam," Thanh Nien newspaper reported.
"I believe that this is worrisome for all foreign companies, especially those with any links, direct or indirect, with China," a foreign diplomat who requested anonymity said.
"I think Taiwanese companies will be especially concerned as they are being dragged into the Vietnam-China dispute even though Taiwan is not the same as China and it is also a claimant to the South China Sea," he said.
Many Taiwanese companies operate from the VSIP.
An executive at one industrial park said the protests began Monday night and by Tuesday had hit four parks which are home to Chinese and other foreign-owned businesses. He said some factories that refused to stop work were vandalized.
Police were present on Tuesday morning, but the protests were continuing, he said. He didn't give his name because of the sensitivity of the issue.
Photos circulating online showed crowds of people pushing over fences at one industrial park and broken windows at a factory
China sent warplanes to protect the oil rig in the South China Sea, reports from Vietnam said Monday.
Two groups of jet fighters flew over Vietnamese ships that have been trying to prevent the installation of the oil rig, according to the Vietnamese coast guard.
The Chinese government and state media did not comment on the reports.
China has deployed dozens of vessels including warships to guard the drilling platform.
Beijing insists the oil rig site is inside its "sovereign territory" near the disputed Paracel islands, which China claims as the Xisha islands.