McGloin on Monday said he was knocked unconscious when he hit his head on the concrete floor of the team's locker room after a brief scuffle with receiver Curtis Drake.
McGloin accepted full responsibility for the fight, which he said included several punches and lasted about 10 seconds.
McGloin hasn't been cleared to practice and could miss the Jan. 2 game against Houston. Penn State interim coach Tom Bradley said both McGloin and Drake face internal discipline.
Penn State police and the school's Office of Judicial Affairs are investigating the incident.
"I started it, but as a quarterback for this university, I should be held to a higher standard," McGloin told reporters at Penn State's bowl media day. "It should not have happened. I should've walked away from it."
Backup Rob Bolden has been working with the starting offense in practice since the fight, although he also faces internal discipline for an incident Friday. Bolden was cited for retail theft for taking a Gatorade bottle from a campus convenience store.
Bolden returned the bottle unopened in what Bradley described as a prank. Bradley said Bolden will be disciplined internally but won't face any playing-time penalties. The sophomore began the season as Penn State's starter.
Another Nittany Lions quarterback, Paul Jones, could be available for the bowl if he's cleared academically. Jones' grades have kept him sidelined this season.
Adam Rittenberg covers Big Ten football for ESPN.com. He can be reached at firstname.lastname@example.org.