Australia open their campaign against Italy on September 11 before playing Ireland on September 17 in their toughest pool match.
Wallabies coach Robbie Deans already has some selection headaches following the Suncorp Stadium triumph but would find it hard to replace the highly-skilled Cooper.
Options would include James O'Connor, who had been stood down from Saturday night's win, a fit-again Berrick Barnes and game-breaking fullback Kurtley Beale.
Cooper's hearing will be chaired by South African official Jannie Lubbe.
After the match Cooper claimed he could not remember making contact with McCaw.
"I can't remember any incident, but that's rugby," he said.
"It's a contact sport. Bodies are colliding left, right and centre. There's a lot of niggle going on out in the field.
"That's why these matches are so good to watch. Australia v New Zealand matches go down in history."
Cooper, who has had a running battle with McCaw since last October's Bledisloe Cup clash in Hong Kong, said he felt privileged to compete against the game's premier open side flanker.
"To have a living legend like Richie McCaw to play against, all the boys love it," he said.
"These games against New Zealand bring out the best of us."
McCaw was diplomatic when quizzed about the latest flash point between the pair.
"I didn't see it but I felt it," he said.
"I don't know if it was intentional or an accident. Someone else will decide that."
- NZPA
