Giteau, who is widely considered as one of the game's leading lights, has been struggling with the injury since taking a heavy knock in the 49-3 win over Fiji last week.
The 27-year-old has been a mainstay of the Wallaby team for the past five seasons having made his debut at Twickenham back in 2002.
Giteau started his career as a scrum-half and had, until now, been chosen regularly at fly-half since Robbie Deans took over as Australia's head coach in 2008.
He was due to start this weekend's first Test in Perth at inside centre, with Queensland Reds pivot Quade Cooper preferred at outside-half.
Berrick Barnes comes into the side in the No12 shirt, with Peter Hynes taking Barnes' place on the bench.
Teenage sensation James O'Connor will take over the kicking duties, five days after he helped himself to 25 points in the Australian Barbarians' 28-28 draw with England's midweek side.