According to the Associated Press, the University of Alabama Police Department incident report shows that Williams was arrested at about 1 a.m. Thursday in his vehicle.
Williams, a senior, has started every game this season and has 1.5 sacks. He is the No. 9 prospect on Mel Kiper Jr.'s Big Board of draft-eligible players.
Coach Nick Saban said in a statement, "This kind of behavior is not condoned in our program. We are currently in the process of reviewing all of the information.
"Once we have a complete understanding of the situation, we will determine what we need to do in terms of the appropriate discipline."
The 6-foot-4, 237-pound Louisiana native came on strong as a junior in 2015, getting 10.5 sacks sacks despite not starting a game.
He is the second Alabama player who has been arrested for a charge involving a gun this year. Offensive tackle Cam Robinson faced felony gun charges in Louisiana during the offseason, but a district attorney declined to prosecute.
The Associated Press contributed to this report.