Italian media speculated that the Argentine - 40 in August - could be out for up to eight months and that, considering his age, the injury could even spell the end of his career.
Zanetti, who is two years older than his coach, dismissed the notion telling Inter's website: "My aim is to return stronger than before. I have to change tyres after many kilometres.
"We will decide when to operate. They haven't told me a recovery time but my career is certainly not over, the important thing is to get better."
"It's a big blow and we really didn't need this injury to Javier," Stramaccioni said earlier.
"Losing him today certainly hurts us in a very difficult moment."
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," Zanetti told Mediaset Premium. "I will overcome this as well."
In the last few weeks, Stramaccioni's team have dropped to seventh in Serie A, ending their hopes of Champions League football next season, been knocked out of the Europa League by Tottenham Hotspur and been beaten by AS Roma in the Italian Cup semi-final.
"It's a curse," agreed defender Andrea Ranocchia, who took the armband from Zanetti in the 17th minute. "We seem to be losing two players a game. It's just incredible.
"With the misfortune that we have been suffering, we just have to give more. We have four games to go and we're in an emergency."
