Memphis athletic director Tom Bowen said he and coach Justin Fuente will review video over the next few days and take "appropriate disciplinary measures." He added in a statement Tuesday: "Hopefully, it will be a learning lesson for both teams."
"I don't know what happened at the end, first of all, so I don't know how upset I am," Fuente said after the game. "I'm sure I'll see it eventually. It's not who we are, it's not what we want to represent. I hope it doesn't take away from an incredible football game, for both sides."
BYU athletic director Tom Holmoe apologized to fans via Twitter.
After DaShaughn Terry's game-clinching interception in overtime Monday, dozens from both sidelines headed toward the middle of the field, with many punching and grabbing.
Cameras showed blood streaming from the face of BYU defensive back Kai Nacua as he came from behind to punch Memphis tight end Alan Cross, who was being restrained by someone from the Tigers' staff, in the head.
"You want them to rise above that and have fantastic sportsmanship," BYU coach Bronco Mendenhall said. "I'm sure if you go back and look, there'll be an instance or two that ignited. Probably the majority wanted to handle it really well."
Memphis president M. David Rudd also issued a statement Tuesday in response to the fight.
"We will provide another statement after the completion of that inquiry," Rudd said. "We have the highest expectations of sportsmanship for all of our student-athletes at the University of Memphis. I am very confident in Tom Bowen and Coach Fuente's leadership and know that working together we will be able to ensure incidents like this do not happen in the future."
American Athletic Conference commissioner Mike Aresco released a statement saying he has been in contact with Memphis officials and the league will work with the school in determining violations of the conference's code of sportsmanship.
"Needless to say, we are extremely disappointed that this happened, as we expect the highest standard of conduct from our student-athletes," Aresco said in the statement.
Memphis is a member of the American. BYU is an independent in football
The Associated Press contributed to this report.