Mannion, who had sparked the 14th-ranked Beavers to a 4-0 start, was hurt while handing off during Saturday's win over Washington State.
The sophomore played the entire game, but a subsequent magnetic resonance imaging exam after practice Monday revealed a knee injury, the coach said.
"It's very disappointing for the young man," Riley said. "He's invested a ton and he's going to miss some time."
The coach wouldn't elaborate on the nature of the injury.
Mannion was averaging 339.5 passing yards, seven touchdowns and four interceptions per game.
Junior Cody Vaz was named the starter behind center for Saturday's contest against Brigham Young.