The 23-year-old, who recently committed his future to the club despite being heavily linked with a move away during the summer, criticised a member of Inter Milan ultra group Curva Nord over an incident when he tried to give a young fan his shirt after a game.
Icardi also claimed that he could bring over a group of criminals from Argentina to kill the Curva Nord, which prompted an angry response from the Inter fans.
"Icardi, as far as we are concerned, you're finished. Why such squalid fiction? We are horrified, that book is ridiculous and with regards to that incident there are only lies. We merely ask for effort and honesty, while he depicts us as threatening figures who gravitate around the club asking for who knows what, so evidently something is wired wrong in his head. An individual like this does not deserve the captain's armband," read a statement from the Curva Nord.
"We don't want to go back over that day when his own teammates hauled him back by the neck to demand a less arrogant attitude towards the Inter population. It is pathetic to read such things talking about us. In his book he writes: 'I am ready to face them one by one. How many are there? 50, 100, 200? OK, record my message and let him listen: I'll bring 100 criminals from Argentina who'll kill them where they stand, then we'll see.'
"He talks about helping little kids, then invents an incident that never happened to make himself seem superior to us, as if it weren't obvious to all that we are the only Curva that helps kids design the choreography in the stands.
"There are no more excuses. We considered him young, a bit of an idiot (like many), but deep down a good lad. Instead this is an individual who cannot be allowed to wear the Inter armband. It's not for us, but Inter simply don't deserve this. You are finished with us. You're done. TAKE THE ARMBAND OFF, YOU CLOWN. Yes, that is what we demand."
The fans also unveiled a banner ahead of this afternoon's match against Cagliari that read: "You are not a man... You are not a captain... You are just a vile piece of shit."
Icardi lined up to take a penalty during the match, but the home fans at San Siro booed him during his run-up and then cheered when he missed.