The 30-year-old will stay in the country for three weeks for recover and is unlikely to play again this season.
Crocked: Woodgate has made just three appearances this season
The England international has made just three appearances this season as medics failed to get to the bottom of the groin problem that has been troubling him for some time.
Harry Redknapp, whose team take on Blackburn at White Hart Lane on Saturday, said: 'Jonathan Woodgate has had an operation today out in Australia, so we are keeping our fingers crossed.
'He went to America and now he's in Australia seeing a specialist there. There were a couple of options but they feel they have the right answer now. The Australian people operated on him at midnight and I will ring him today to see how he is.
'There's no chance he will play again this season, though. He's going to spend the next three weeks in Australia recovering with the specialist.'
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