Stankovic had surgery on his tendon at the end of last season and was expected to recover in time to start the new season in the Nerazzurri team.
However, the 34-year-old will now have another procedure to clean the tendon and speed his recovery.
"It is a problem that has long plagued me and was not completely solved with the first surgical procedure," Stankovic said to SFF.
"In consultation with the medical team at Inter, as well as on the basis of new detailed checks, we decided to go for further surgery. This was the only good solution.
"Previously, I did not want to talk in public because I was waiting for only one thing - to get back on the pitch. Unfortunately, I will have to wait a little longer."