"Stirling was concussed last weekend," said Wallabies head coach Robbie Deans.
"We had hoped that, with time, the symptoms would resolve themselves, but that hasn't happened soon enough for this match, so we've made the call (to leave him out) early."
Kiwi skipper McCaw missed both Tri Nations matches against the Springboks earlier this month as a result of an ankle injury but the 27-year-old openside has been pencilled in for the much-talked about clash in Sydney.
McCaw was expected to miss his country's opening four rounds of the competition but Graham Henry has selected the inspirational Canterbury Crusader in the No7 shirt, although Daniel Braid has also been named in case McCaw isn't yet ready for Saturday's encounter.
New Zealand side to face Australia on Saturday, July 26
Muliaina, Tuitavake, Kahui, Nonu, Sivivatu, Carter, Ellis; Woodcock, Hore, Somerville, Thorn, Williams, So'oialo, Braid/McCaw, Kaino
Replacements: Mealamu, Afoa, Boric, Lauaki, Cowan, Donald, Smith