The cleric, Mohammad Karim, has claimed that the girl was offered to him as a gift by her father while he was teaching her, Tolo news reported on Friday.
The girl's family claims the cleric abducted her.
Police said the victim was kidnapped by the cleric from Herat a month ago.
Karim, who is now in police custody, told police they married on the first night of Eid ul-Fitr.
"We formally got engaged, her family told me to take her anywhere you want," Karim said.
Police officials have said the girl's family accused the cleric of abducting their child a month ago from Obah in Herat.
"The family of the girl rejected the claims that they married; the family said that the girl had been lost, the victim's father and mother are now on their way to Ghor and we hope that they arrive soon so that the police can get to the bottom of the issue," a police official said.
Ghor women's affairs department has condemned the incident.
The victim is being cared for at a safe house and children and women rights groups have pledged to seek justice for the victim, Tolo news reported.
"For now, the department of women's affairs cannot issue a verdict on the case, we are determined to make the case clear," said Masooma Anwari, Head of Ghor Women's Affairs Department.
The reports come amid a rise in violence against women and girls. Reports indicate that in the past 15 years, 95 per cent of all criminals involved in such acts in the country were not prosecuted.
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