The collision happened Saturday night as both Arizona Diamondbacks and Arizona Rattlers games were ending.
Phoenix police say the SUV's driver, 38-year-old Guadalupe Cobos Jr., showed signs of impairment and fled the scene on foot.
The extent of the passenger's injuries wasn't available, though police say they complained of pain and were brought to a hospital as a precaution.
Police say Cobos ran a red light before colliding with the train and managed to run away.
An Arizona State University police officer eventually arrested Cobos about four blocks away.
There was no phone listing for Cobos.
It wasn't known whether he has a lawyer.
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.