Mannion played the entire game against the Cougars but didn't play well, throwing three of his four interceptions of the season in a 19-6 win for the 10th-ranked Beavers.
"It's very, very disappointing for the young man. He's invested a ton and he's going to miss some time," Riley said. "Like I told him, 'You're going to be fine. I read about a guy who hurt his knee in the first game of a the season a few years ago and he's still pretty good -- Tom Brady. The football stuff happens, you've just got to live with it and get better from it.'
"He'll be back and he'll be fine."
Mannion had an MRI on Sunday, but no details were provided about the nature of his injury. Riley did indicate that Mannion will require surgery, but added no further details on the timing of the surgery or recovery.
"I'm going to let the doctors talk about that, or Sean, when he's ready for that," Riley said.
Junior Cody Vaz will replace Mannion against BYU this weekend.
"Cody is a good quarterback. He has been preparing for this for a long time," Riley said. "He'll be good and we'll be ready to go."
Vaz last saw game action in 2010 when he completed six of 17 passes for 48 yards.
"You have to prepare yourself. You have to have a good mental approach," Vaz said. "That's what I've been doing for the past five weeks like I'm the starter. And now that I am I've got to make the most of this opportunity."
Mannion completed 63 percent of his passes for 1,358 yards with seven touchdowns.
Under Mannion, the Beavers have the Pac-12's fourth-rated offense, averaging 459.5 yards per game and the league's No. 2 passing attack. Mannion, along with Arizona's Matt Scott, are the only two Pac-12 quarterbacks averaging more than 300 yards passing per game.
The Beavers (4-0, 3-0 Pac-12) went 3-9 last year but have been one of the nation's big surprises this fall, climbing the rankings after wins over Wisconsin, UCLA, Arizona and Washington State.
ESPN.com's Kevin Gemmell and The Associated Press contributed to this report.