Right activists say there has been a sharp rise in violent attacks against women in the deeply conservative Muslim country, where women have fought hard to gain rights after the collapse of Taliban government in 2001.
Restoring women's rights after the Taliban was ousted by a U.S.-led coalition of troops was cited as one of the main objectives of the war.
The provincial head of women's affairs, Khadija Yaqeen, told Reuters that the girl had told her parents four months ago she had been assaulted.
The father invited the mullah to his house on Monday for dinner, police said.
"I cut off his ears and nose," her father Abdul Qahar, dressed in a traditional shalwar kameez and a turban, said from the police chief's office in the northern Baghlan province.
"I don't know if a cat ate his ears, but his nose went down the drain," he told Reuters, speaking in the Dari language
Police arrested the girl's parents on Tuesday. Ahmad Jawid Basharat, a police spokesman in Baghlan, said Qahar had tied the cleric's hands and feet and cut off his nose and an ear as an act of revenge.
The 32-year-old cleric denied he had assaulted the girl. Police said they have opened a case against him.
Religious, or sharia, law often holds sway over constitutional law in some parts of rural Afghanistan.
"If there was a functioning rule of law, then he would be punished even more severely," said the girl's mother, Sultana, wearing a traditional all-covering burqa.
There is growing fear among many people in Afghanistan that the withdrawal of NATO-led forces and efforts to reach a political agreement with the Taliban to end the 12-year-old war could undermine hard-won freedoms for women.
The hardline Islamist government banned girls from attending school when it ruled the country from 1996 to 2001, and during the insurgency its militants have regularly bombed girls' schools built with U.S. money.
Afghan couple hack off nose, ears in revenge attack | Reuters (external - login to view)