The 29-year-old suffered a recurrence of the injury in the Wallabies' 67-5 victory over the United States and a scan revealed he will be sidelined for six weeks.
Australia, who are having to contend with a lengthy injury list, are likely to delay naming a replacement until after their final Pool C fixture against Russia in Nelson on Saturday.
"It's bad luck for Wycliff," said coach Robbie Deans. "Unfortunately his previous history of injury in this area has impacted on the length of time required for his rehabilitation."
Full-back Kurtley Beale, one of the stars of the World Cup so far, will miss the clash with Russia after incurring a minor hamstring strain against the USA, but is expected to return for the quarter-finals.
Centres Pat McCabe (shoulder), Anthony Fainga'a (head) and Rob Horne (cheek) also left the field during Australia's third pool match.
McCabe and Horne have been pencilled in for returns in the quarter and semi-finals respectively, while Fainga'a is following concussion protocols and could be available for Russia.
Winger Digby Ioane should participate in the likely last-eight showdown with South Africa as he continues his rehabilitation from the dislocated thumb sustained in the Wallabies' opening match of the tournament against Italy.
Flankers David Pocock (back) and Scott Higginbotham (back), wing James O'Connor (hamstring) and lock James Horwill (shoulder) are all expected to be available for Russia.
Lock Dan Vickerman has been cleared of any problem to his leg.
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