Karr, 42, claimed in August 2006 that he was with Ramsey when she was killed in Colorado at age 6, in a 1996 case that remains unsolved. DNA testing cleared Karr in the Ramsey slaying.
Police arrested Karr Saturday morning at the Sandy Spring, Ga., home of his father, Wexford Karr, after receiving a 911 call, The Atlanta Journal-Constitution reported.
The elder Karr, 86, said he called the emergency number to quell an argument between John Mark Karr and his girlfriend, Brooke Simmons, 22.
Police found enough evidence at the home to book John Mark Karr on charges of battery against his father and obstruction of a 911 call, the newspaper said.
The elder Karr told the newspaper the fight was minor and his son should not have been arrested.
"Nah, he didn't hurt me," Wexford Karr said. "I'm too tough for a little whippersnapper kid to hurt me."
John Mark Karr was set to appear before a judge Sunday, the newspaper said.