Orgeron made the announcement after a late-afternoon practice as the Trojans continued preparations for Saturday's Pac-12 Conference game at California.
Morgan, a fourth-year junior, had been slowed by injuries since last spring and had not played this season.
Morgan had two previous knee operations.
He had major reconstructive surgery after suffering an injury while playing at Woodland Hills Taft High. He also had an arthroscopic procedure early last season.
Morgan rushed for 163 yards as a freshman and 201 as a sophomore in 2012.