Notre Dame football players Ashton White, Max Redfield, Kevin Stepherson Jr., Dexter Williams and Te'Von Coney were arrested on the night of Aug. 19.
Per Brandon Pope of ABC 57, all five players face a misdemeanor charge of marijuana possession, with Redfield, Stepherson and Williams also facing a charge of possessing a handgun without a license.
The arrests occurred at 10:07 p.m. following a traffic stop by an Indiana state trooper.
According to ESPN.com, the car was clocked going 73 mph in a 60 mph zone. The officer "reported smelling marijuana coming from the car, and a police dog indicated that there were drugs in the vehicle."
Kelly said on Wednesday the University would determine the punishment for the suspended players, per ESPN.com's Brian Fortuna.
Redfield is the most prominent Fighting Irish player involved. He has been the starting safety the last two seasons, finishing fourth on the team in 2015 with 64 total tackles and recording one interception.
Williams appeared in seven games last season at running back, carrying the ball 21 times for 81 yards and one touchdown.
Early Saturday morning in a separate incident, senior cornerback Devin Butler was arrested on two preliminary charges of battery against law enforcement and resisting law enforcement.
Notre Dame, ranked No. 9 in the preseason USA Today Sports Coaches Poll, will open the season Sept. 4 against Texas.