The murder took place two days ago in Kunduz province. The baby girl, who is now two months old, was not hurt.
The birth of a boy is usually a cause for celebration in Afghanistan but girls are generally seen as a burden.
Some women in Afghanistan are abused if they fail to give birth to boys. And this is just the latest in a series of high-profile crimes against women in the country.
Late last year a horrifying video emerged of the injuries suffered by a 15-year-old child bride who was locked up and tortured by her husband.
'Crime against humanity'
This murder took place in the village of Mahfalay, in the district of Khanabad in Kunduz.
Khanabad's police chief, Sufi Habib, told the BBC that "the mother gave birth to a third girl two months ago. The husband and mother-in-law strangled her for giving birth to a third daughter".
Senior officials told the BBC that the mother-in-law, known as Wali Hazrata, tied the feet of the 22-year old woman, who was known as Stori, while Stori's husband strangled her.
He is thought to be a fighter with an illegal armed militia which is believed to have some political support. Local villagers say that Stori often urged her husband to lay down his arms.
"She lived in a hell not a house. But then she also asked her husband to stay home and avoid going out with these thugs," one neighbour who wished to remain anonymous told the BBC.
While militia groups have some political support, they have often been accused of violence against women, robberies and extortion.
Afghan women's rights activists brought this case to the attention of the media.
The Director for Kunduz Women's affairs, Nadira Gya, condemned the incident saying: "it was a brutal crime committed against an innocent woman".
Local religious and tribal elders in the district also condemned the killing, saying it was an act of ignorance, and calling it a crime against Islam, humanity and women.
They called for immediate punishment. Wali Hazrata appears to have made no public comment as yet.