The body of the girl called Hameya, whom authorities estimate was aged between seven and 10, was found on Sunday night, said Naqibullah Amini, police spokesman for the northwestern province of Badghis.
Hameya's husband was on the run from police and her father had been detained for questioning, Amini added.
Provincial governor's spokesman Jamshid Shahabi said Hameya was married under a tradition known as "badal", when girls are exchanged between two families as brides.
Badal enables both families to reduce the cost of marriage by avoiding paying a dowry.
After the other girl in the arrangement was killed by her own husband, Hameya's husband began to torture her in revenge and eventually killed her, Shahabi told AFP.
Hameya's husband, whom officials said was aged between 20 and 30, already had at least one wife, according to Lailuma Noorzad, head of the provincial women's affairs department.
Hameya had been married for six months, officials said.
The legal marriage age in Afghanistan is 16 for girls and 18 for boys, according to the United Nations.
But the traditional practice of marrying children still persists in the conservative and patriarchal country, largely due to poverty and insecurity.
At least one in three Afghan girls is married before they turn 18, the United Nations Children's Fund said in a recent report.
