The Post-Courier newspaper said the 18-year-old chopped her father's head clean off after he repeatedly raped her last Tuesday night in their village in the poverty-stricken Pacific nation's Western Highlands.
The report cited a pastor as saying the father, in his mid-40s, had three other children and raped his daughter when they were alone in the house after the mother and the other siblings visited relatives.
"The father wanted to rape his daughter again in the morning inside the house and that was when the young girl picked up the bush knife and chopped her father's head off," he said.
Community leaders are now refusing to hand the girl over to police, vowing to protect her.
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"The people and leaders in our area went and saw the headless body of the father after the girl reported the incident to the leaders and the people and told her story of why she had killed her father," said Kumi.
Violent crime, as well as witchcraft, is rife in Papua New Guinea with the government last month voting to revive the death penalty in a bid to deter offenders after a series of high-profile grisly incidents.
Brutality against women, including domestic violence and rape, is also endemic in the country.