The 39-year-old Argentine snapped his Achilles tendon in the first half of the Nerazzurri's 1-0 away defeat to Palermo in Serie A and could be sidelined for up to eight months.
"At a certain point I felt a pull and it hurt so much. It still does," he told Mediaset Premium. "I will overcome this too."
Coach Andrea Stramaccioni added on Sky Sport Italia: "There's an injury to the Achilles tendon of his left foot.
"It's a big blow and we really didn't need this injury to Javier. Losing him today certainly hurts us in a very difficult moment."
Zanetti's current contract with Inter runs out at the end of the season but he has long said that he wants to play for the Italian club for at least one more year.