Arizona Department of Public Safety officials say the man was arrested about 5 p.m. Tuesday inside a store at the Arrowhead Town Center.
The man's name hasn't been released yet.
A DPS officer tried to stop a motorcycle rider for speeding near the interchange of Interstate 10 and I-17.
The driver refused to pull over and that started a chase. Officers in a helicopter followed the driver to the mall.
DPS officials say the motorcycle driver changed his clothes while inside a second-floor store at the mall.
The man was arrested as he tried to take the elevator back to the mall's first floor.