Inter said on Monday the 23-year-old would be sanctioned over comments in the book but would not be stripped of the captaincy.
But the Curva Nord hardcore supporters criticised the decision, posting a statement on their website, saying: "Icardi is not our captain, not now or ever."
Icardi has been Inter's top scorer for the past two campaigns and is again this season.
But he has upset some fans after an account in his book about a confrontation with one of the ultra leaders in 2015 in which he claimed the fan ordered a child to hand back the Argentine's shirt after the player had given it to him.
The ultras say Icardi's version of events is an invention.
On Sunday he was greeted by several insulting banners at San Siro as he took to the pitch for Inter's Serie A game against Cagliari, which they lost 2-1.
He also missed a penalty during the match -- which the Inter fans applauded.
The fans said the incident would not affect their support for the rest of the team, who have slumped to 11th in Serie A.
"Inter need us," the statement said.
(Writing by Brian Homewood,; Editing by Neville Dalton)
