The 33-year-old midfielder, who has struggled for form and fitness this season, requires surgery, meaning his campaign is over
The club released a statement on their official website revealing that the former Serbia international requires surgery on his Achilles tendon, thus ruling him out of Sunday's Milan derby and next week's trip to Rome to take on Lazio.
However, it was not disclosed just how long Stankovic, who has made 19 appearances for Inter this season, will be out of action for.
Inter were already reeling after seeing their six-game undefeated run under interim coach Andrea Stramaccioni ended with a 3-1 defeat to Parma at the Ennio Tardini on Wednesday.
That loss means that the Nerazzurri remain sixth in the standings, three points adrift of Napoli, who occupy the third and final Champions League place.