Parisse in race against time
The charismatic No.8 returned to the National side last weekend in a warm-up match against Wales in Cardiff but sustained a knock to his left leg in the 19-23 defeat.
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The surgery took place in Paris where the 31-year-old Argentine-born flank had a swelling of clotted blood drained.
Further details on his expected absence would be revealed following tests "in the coming days".
There is also concern about the fitness of Luca Morisi and Gonzalo Garcia, who left the field in Cardiff with sprains. An update on their progress is expected to be announced by Wednesday, September 9.
Italy open their World Cup campaign against France in Twickenham on September 19.
AFP