The body of Miri Clare Nyongere was in a forest, with injuries to the neck, neck and genitals, said Celine Ndabupaha, an administrator in Kiganda province.
The motives behind the killing of Nyongere, who left four children behind, were not known.
The Burundi Freedom Congress party has consistently condemned violence against its members ahead of the 2020 presidential election.
In August 2019, another party member, Nsafiumwami Gregory, was killed in an attack by a group of gunmen with axes.
A UN Human Rights Council report released in September 2019 said that "serious human rights violations occur in Burundi against members of the opposition and their families by government forces and the youth wing of the ruling party (Imbonirakuri).