According to the Sheriff Department website, Smith was arrested Saturday morning and placed in the Tuscaloosa County Jail on $1,000 bail.
Smith was also arrested on a DUI charge in August 2013. Crimson Tide coach Nick Saban announced he was suspended for at least one game at the time, and Smith didn't play in the first two.
Saban wasn't available to the media after Saturday's practice.
No further details were immediately available. Campus police referred a request for information to university relations.
Smith is battling for the starting job at free safety. He had 56 tackles last season.