Le Thi Tuyet Mai, 67, doused herself with petrol and set it alight in front of the landmark Reunification Palace in Ho Chi Minh City early Friday, the website of the Thanh Nien newspaper quoted an official in the city as saying.
"The fire was extinguished by security guards there after three minutes, but the woman died," the official, Le Truong Hai Hieu, said.
The report said authorities found a can of petrol at the scene and a note in which Mai expressed indignation over the Chinese oil rig and called for its removal.
A video clip of the incident circulated on YouTube.
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The woman's son also was quoted as saying "she seemed to be sad, frequently following news on TV" about the Vietnam-China dispute.
China deployed the giant deep-sea drilling rig in early May, sparking tense confrontations at sea between dozens of Chinese and Vietnamese vessels.
The two countries hotly dispute sovereignty of the area, and the confrontation sparked anti-China riots in Vietnam last week.
China -- which has evacuated thousands of its nationals from Vietnam over the riots -- says four Chinese citizens died in the violence. Vietnam says three Chinese were killed.
Vietnamese Prime Minister Nguyen Tan Dung said on Wednesday that the deployment of the rig by China had "seriously threatened peace".