The arrest at 1:13 a.m. marked the second in less than two months for Fairley, the Lions' first-round pick a year ago, the Detroit Free Press reported.
He was arrested April 3 on a misdemeanor marijuana possession charge after a traffic stop near his home in Mobile, Ala.
On Monday, the Alabama Department of Public Safety said in news release, Fairley was driving his 2010 Cadillac Escalade at more than 100 mph when he passed a police car patrolling westbound I-10 in the Mobile area.
Police said Fairley initially refused to stop after the patrol car activated its emergency lights and siren and "showed signs of impairment" when he did stop.
Fairley, who refused a Breathalyzer test, was also issued traffic citations for reckless driving, no proof of insurance and an open container, police said.
WALA-TV, Mobile, reported Fairley was released just after 9 a.m. Monday after posting $1,750 bond.
In a statement, the Lions said, "We are aware of the reports and are in the process of gathering more information."
Brian Overstreet, Fairley's agent, did not return a phone call seeking comment, the Free Press said.