The 32-year-old travelled to Miami in a bid to cure a recurring injury problem, although his future at San Siro remains far from certain due to a lack of playing time
The 32-year-old has suffered a number of problems with his foot, including facing a short absence after sustaining 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 the Nerazzurri.
His lack of playing time has forced Chivu down the pecking order at Inter, leading to speculation that Dinamo Moscow could swoop for his signature as his contract enters his final year - although the defender himself has insisted he has no desire to leave the club.
Chivu joined Inter for €16 million [£13m] from Roma in 2007, and was part of the treble-winning squad under Jose Mourinho in 2009-10.