The 39-year-old Argentina international will now undergo an MRI scan but there are suggestions he could be ruled out for eight months, which at his age may signal the end of his career.
Zanetti has made more than 800 appearances for Inter, including over 600 in Serie A, since joining the club from Banfield in 1995 and has never before suffered a serious injury.
He has won five Serie A titles, four Italian Cups, one Champions League, one UEFA Cup and one Club World Cup and is also Argentina's most capped player.
"I felt a pull at one point, I'm not sure if anyone touched me, and it really hurt. I will overcome this as well," said Zanetti.
Inter coach Andrea Stramaccioni added: "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."
Inter, who have dropped to seventh in Serie A, have suffered a string of injuries in recent weeks and were missing Rodrigo Palacio, Diego Milito, Walter Samuel, Antonio Cassano, Walter Gargano and Fredy Guarin for the trip to Sicily.