Davis, a junior, is alleged to have committed battery on a woman he was dating on four occasions between May 2017 and this past June, according to an arrest warrant issued Friday by LSU Police.
The woman told police Davis punched her hard enough to fracture one of her ribs in one instance, began to strangle her in another and later texted that he might kill her. The warrant says police obtained the text and photos of bruising.
It's unclear whether Davis has an attorney. He was being held in the East Baton Rouge Parish Prison without bond on Saturday.
Davis played in all 13 games for LSU last season, catching three passes for 134 yards and two touchdowns, including an 87-yard score against Syracuse. He also caught one pass for 19 yards in 2016.
ESPN's Adam Rittenberg and The Associated Press contributed to this report.