She was protesting against the detention of her daughter, Ta Phong Tan, who is facing charges of anti-state propaganda, another daughter told the BBC's Vietnamese service.
Dang Thi Kim Lieng set herself alight in southern Bac Lieu province.
Her daughter faces trial in August and could be jailed for 20 years.
Dang Thi Kim Lieng went alone, without telling anyone, to the local government building in Bac Lieu, the second daughter told the BBC.
The police have made no comment, but activists and lawyers said that Mrs Dang died while being taken by police to a hospital in Ho Chi Minh City.
She was said to be extremely worried about the fate of her daughter, who she had not seen since her arrest last September.
Ta Phong Tan was arrested by the authorities with other bloggers, who are also accused of subversive activities in a state that controls the media and has little tolerance for criticism.
She is a former policewoman who built up a following with her reports on police abuses and injustices in the legal system.
The police newspaper denounced her writings as toxic and she was charged with distorting the truth and denigrating the Communist party and state.
Ta Phong Tan had posted a large number of articles on the "Free Journalists' Club", a banned website that has been a focus of the government crackdown on its internet critics.
She denied all the charges against her and has remained in detention since her arrest.
She was due to stand trial alongside another famous blogger, Phan Thanh Hai, who wrote about various sensitive issues, including a dispute with China over maritime boundaries, alleged corruption and case studies of famous dissidents.
Human Rights Watch has accused the Vietnamese government of stepping up its repression of dissidents over the past year and of jailing dozens of peaceful activists.
It said Mrs Dang's apparent suicide looked like an act of desperation to show the authorities what they were doing to the families of dissidents.
The mother of a prominent Vietnamese blogger has died from her injuries after setting herself on fire in front of government offices, her family says.