Both were projected starters and had been under investigation for their ties to a local luxury rental car agency.
In a statement, the university said it arrived at the decision after outside consultation, including discussions with the NCAA enforcement staff, but would continue the players' financial aid through graduation.
"As no staff members or boosters were involved in the violations, the program will not be subject to sanctions and, at this time, the University deems this matter closed," the statement said.
Muhammad, a redshirt junior, had his share of issues during his Miami career, serving a suspension for all of 2014 because of an off-campus fight. He also was suspended for the season opener last year for team rules violation. Grace, a senior, started 10 games last season and finished third on the team with 79 tackles.
Another player implicated in the allegations, linebacker Juwon Young, had been suspended indefinitely and opted to leave the team. He signed with Marshall.
Receiver Stacy Coley has also been a part of the school's investigation, but there's no word yet on whether he will face punishment.