The 32-year-old former Glasgow Rangers and Newcastle United player was diagnosed with cancer last week and underwent the procedure on Tuesday.
He will miss the World Cup qualifier in Bahrain on November 19.
Socceroos coach Pim Verbeek said: "It's always a shock to hear of a diagnosis like this but I am encouraged by the prognosis from the medical practitioner.
"I speak for the entire team in wishing him a speedy recovery," he added.
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