Vannacci, 54, a veteran of the Afghanistan and Iraq wars, was dismissed as head of Italy's Military Geographical Institute, a post he took up in June, Italian news outlets reported.
Questioned by AFP, the defence ministry did not deny the information.
Military officials said "The World Backwards" had been self-published earlier in August on Amazon.com without the knowledge of the army.
Among various opinions expressed in the book, Vannacci says homosexuals are not "normal" and rails against the "dictatorship of minorities," taking aim at feminists, environmentalists, people of colour, and immigrants.
He describes Italian volleyball star Paola Egonu, who is black, as "Italian by citizenship, but it is clear that her features do not represent Italian-ness".
Defence Minister Guido Crosetto had announced on Thursday that disciplinary proceedings would be opened against Vannacci.
He said in a statement: "The personal ramblings of a general, even if still in service, should not be used in any way to polemicise against the Defence [Ministry] and the Armed Forces".
He added that the general had "expressed personal opinions that discredit the Army, Defence and the Republican Constitution"
Crosetto is one of the co-founders of the right-wing party Brothers of Italy, led by Prime Minister Giorgia Meloni.
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