The two attackers burst into the home of the widow and her daughter in Ghazni city at around 4:00 am and shot them dead, said Ghazni provincial police chief Zilawar Zahid.
The killings are the latest to highlight the dangers which many women in Afghanistan face 10 years after a US-led invasion ousted the Taliban's harsh regime which enforced repressive policies against women.
"They were killed inside their house," said Zahid. "An investigation is under way to find out why they were killed and Afghan police have arrested two men in connection with the case."
He denied media reports that the women were stoned to death.
A man who lived near the women, Mohammad Jan, said the women had been "accused of adultery and immoral activities."
Women's rights have improved in some parts of Afghanistan since the Taliban were forced out of power, but many still face violence, particularly in areas where the militant Islamists remain powerful such as Ghazni.
The Afghan Independent Human Rights Commission logged 1,026 cases of violence against women in the second quarter of 2011 compared to 2,700 cases for the whole of 2010.
And 87 percent of Afghan women have experienced physical, sexual or psychological violence, or forced marriage, according to figures quoted in a report by the charity Oxfam last month.
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