The Bucs made it official later in the day when they placed McCoy on season-ending injured reserve.
Morris said McCoy suffered the injury while reaching out with his right arm to make a tackle during Sunday's 27-16 loss to the New Orleans Saints.
"You lose the get-off, the explosiveness," Morris said. "You're talking about a guy that gets off the ball and causes disruption. ... He's done a great job for us versus the run."
The St. Petersburg Times reported after the game that McCoy was done for the season but cited only "players" as the source.
McCoy, the No. 3 overall pick in the 2010 NFL Draft, missed the previous two games with a left ankle injury. He also missed the final four games of last season with the same injury he has now but in his left arm.
"He's got to come back, he's got to rehab and be ready to play a 16-game season," Morris said.
The injury leaves just two players on the roster who are listed as true defensive tackles: 2010 second-round draft pick Brian Price, the club's other starting tackle, and backup Roy Miller. The Bucs also used their first two picks in the 2011 draft on defensive linemen, selecting ends Adrian Clayborn and Bowers.
"Hopefully we can get Frank (Okam) back this week. He had the (calf) strain last week in practice and we have to see where he is health wise. That is an issue right now," Morris said, adding it's not ideal to move one the team's backup ends inside to replace McCoy.
The Associated Press contributed to this report