The 32-year-old has had a number of problems with his foot, including facing a short absence after suffering a dislocated toe last year, and the current operation marks his third bout of surgery.
Those injury problems have seen the Romania international limited to just 24 appearances in Serie A over the previous two seasons for Walter Mazzarri's side.
His lack of playing time has forced Chivu down the pecking order at Inter, with speculation that he could be on his way out of San Siro with his contract due to expire in June 2014.
Dynamo Moscow have been linked with a move for the veteran defender, with his agent hinting at the possible early termination of his Inter contract to allow a move to the Russian Premier League.
Chivu joined Inter from Roma in 2007 and made at least 20 league appearances every season prior to the 2011-12 campaign when his injury woes set in.
