The murdered woman’s husband, a member of a local militia, is also suspected of involvement but he has since fled.
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.
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.