Zanetti said that the operation was a success and that the support he has received will drive him on to return to his best.
"I'm fine," Zanetti told the club's official website. "The operation has been completed and now my recovery is even closer than before.
"I have to thank Doctor Benazzo, Doctor Combi and all the medical staff of the Policlinico in Pavia who have treated me very well and have made me comfortable here. Now the rehabilitation has already begun.
"I've received many messages of support towards me, not only from the world of football, but also from all over the world of sport. It's made me incredibly happy. Even when I went into the operating room I could hear the fans outside cheering me on, and they even had a banner for me."
Inter face Napoli on Sunday in Serie A.