Nadia Anjuman, 25, died late Friday, said provincial police chief Nisar Ahmad Paikar. "We have arrested her husband, accused of killing her," Paikar told AFP. The couple had a six-month-old daughter.
Her husband confessed to the beating but denied that he had killed Anjuman, he said.
"She was especially famous among the female poets in Herat," said a lecturer at Herat University, Ahmad Sayeed Haqiqi.
The editor of the Itfaq-e-Islam daily newspaper, Naqib Arween, said Anjuman had this year published a collection of her poems calls Gul-e-dodi, which means dark red flower.
The United Nations condemned the killing. "The death of Nadia Anjuman, as reported, is indeed tragic and a great loss to Afghanistan," UN spokesman Adrian Edwards said at a media briefing.
"It needs to be investigated and anyone found responsible needs to be dealt with in a proper court of law," Edwards said.
Under the fundamentalist Taleban regime of 1996-2001 women were denied the right to education and could not even leave their homes without a male member of the family.
Women have been given more freedom since the Taliban were toppled in a US-led campaign in late 2001. But rights groups say they are still mistreated by men, including through sexual and domestic violence.