The 25-year-old Mobile native was taken to the Mobile County Metro Jail shortly before 7 a.m. and was released on a $350 bond, according to the jail log.
Airport Police Chief James Kincaid would not say what led to Peavy's arrest, but he told the Press-Register newspaper that "a situation presented itself and the officers involved felt like they had a situation to deal with."
Padres general manager Kevin Towers told The Associated Press he was told that Peavy was headed for a goodwill tour of the Dominican Republic with other major league players when he double-parked to drop off his bags and was told by airport police to move his car.
"The airport police told him he couldn't park his car there and he said, 'Write me up a ticket and I'll pay for it,'" Towers said. "He was arrested."
A message left on Peavy's cell phone wasn't immediately returned. Peavy's agent, Barry Axelrod, didn't respond to an e-mail and a call to his cell phone.
Kincaid said the incident occurred around 5:20 a.m. just outside the terminal building.
Peavy has a career record of 57-45, all with the Padres. He was 11-14 with a 4.09 ERA last season.