The woman, Aisha, gained worldwide attention when she appeared on the Aug. 9 cover of Time magazine.
Under orders from a Taliban commander acting as a judge, she was disfigured last year as punishment for fleeing her husband's home, according to Time's story in August and other accounts.
Just 18 years old at the time, Aisha said she ran away to escape her in-laws' beatings and abuse.
Afghan Interior Ministry spokesman Zemeri Bashary said Aisha's father-in-law was arrested in southern Afghanistan in recent weeks. It was not immediately clear whether he had been formally charged.
He was being held in jail in Uruzgan province.
Aisha was sent to Los Angeles over the summer for reconstructive surgery. In September, she was fitted with a temporary, prosthetic nose so she could visualize what she would look like and to help build her confidence. AP
