The federation added that further details on the player's expected absence would be revealed following tests “in the coming days”.
The 31-year-old Argentine-born flanker has 112 caps for Italy and is their star player.
The surgery in Paris was to drain a haematoma – a swelling of clotted blood – in a muscle in his left leg, after he picked up a knock in Italy's World Cup warm-up Test defeat to Wales in Cardiff last weekend.
Italy open their World Cup campaign on September 19 in Twickenham against France.
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