In a statement released earlier in the day, LSU coach Ed Orgeron announced that Parker, a redshirt freshman, had been suspended indefinitely for violation of team rules.
According to the affidavit of probable cause, Parker allegedly got into an argument with his girlfriend around 1 a.m., pushing her into a dresser and leaving a mark on her hip, which the responding officer later observed.
Parker allegedly threw items around her apartment, including an iPhone that shattered.
The criminal damage to property is a felony.
LSU is scheduled to open the season at home against Mississippi State on Sept. 26.