Storay, 30, was beaten to death in the Khan Abad district of the northern province Kunduz a week ago after she delivered another baby girl, angering her husband who had wanted a son.
"She was beaten to death by her husband after she gave birth to their third baby girl. We were informed of the case by Storay's father," Sayed Sarwar Husaini, the provincial police spokesman, quoted by news agencies. There were signs of torture on her body, he added.
According to Sarwar, the police have arrested Storay's mother-in-law in connection with the case, but her husband has fled.
"Police are searching for him," he said.
Violence and abuse against women continues to be a major problem in Afghanistan, a long decade after US-led military brought down the Taliban regime.
Last month, police found a teen bride who had been locked in a toilet for six months at her husband's house in Baghlan province. She was burned and beaten, and had her fingernails pulled out, police said.
British charity Oxfam says some 87 percent of Afghan women report having experienced physical, sexual or psychological violence or forced marriage. Meanwhile the Afghan Independent Human Rights Commission mentioned that 1,026 cases of violence against women in the second quarter of 2011 compared with 2,700 cases for the whole of 2010.[AGENCIES]