The Tuscaloosa County Sheriff's Department's online records show the sophomore for the top-ranked Crimson Tide was arrested Sunday and jailed on $1,000 bond. He had not been released as of Sunday afternoon.
Tuscaloosa police referred questions to spokesman Sgt. Brent Blankley, who did not immediately return a call.
Smith played in all 13 games as a freshman during last season's national championship run, and his role on the nation's top defense increased late in the year.
He was expected to compete for the starting job vacated by top-10 draft pick Dee Milliner.
Crimson Tide coach Nick Saban said in a statement that he "will handle it appropriately once I've had a chance to review the information."