Floyd had blood-alcohol levels more than twice the legal limit during his Sunday morning incident, authorities allege.
"I've spoken to Michael Floyd and his mother and, in light of what took place this past weekend, I let him know he has been suspended indefinitely from football team-related activities," Kelly said.
"I want to apologize to my family, friends, teammates, coaches, the university and the extended Notre Dame family for my behavior this weekend," Floyd said in a statement issued Monday.
A probable cause affidavit filed by St. Joseph, Ind., County Deputy Prosecutor Chris Daniels alleged Floyd registered a blood-alcohol level of 0.19 percent after being pulled over Sunday morning near the Notre Dame campus, The (Fort Wayne, Ind.) Journal Gazette.
The affidavit said Floyd failed three field sobriety tests after before being charged with operating a motor vehicle while intoxicated and booked in the South Bend, Ind., jail.