The number eight had the procedure in Paris after sustaining bruising in Italy's defeat by Wales in Cardiff on Saturday, their final warm-up game before the global showpiece starts next week.
Parisse, 31, has been capped 113 times by Italy and is a towering presence at the back of the scrum.
"In the coming days we will broadcast updates on the recovery time of the player," the FIR said in a statement.
Italy are also monitoring the fitness of centres Luca Morisi and Gonzalo Garcia who were both forced off with sprains against Wales.
Italy are in World Cup Pool D along with Ireland, France, Canada and Romania. They open their campaign against the French at Twickenham on Sept. 19.
(Reporting by Justin Palmer; editing by Ed Osmond)
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