The school says the suspension is for an unspecified violation of team rules. In a statement Monday, coach Larry Fedora said he hopes Morris ''will learn from his mistake'' and make better decisions.
UNC (4-5, 2-3 Atlantic Coast Conference) is off this week.
Chapel Hill police stopped the 22-year-old early Sunday for failing to stay in his lane and arrested him, according to arrest and incident reports. Morris was released to a sober person on a written promise to appear in court Nov. 13.
Morris is the team's fourth-leading rusher with 162 yards and four touchdowns. He has 17 catches for 146 yards.