"I would like to remind you that incitement to hatred on the basis of gender is a criminal offence.
"Consequently, I ask you to remove this book from your catalogue immediately or face criminal prosecution."
The book's publisher, Monstrograph, deny the book is an incitement to hatred. Colline Pierré, one of the founders of the volunteer-run "micropublisher", said: "The title is provocative but the language [is] measured.
"It is an invitation not to oblige oneself to frequent men or compromise with them. At no time does the author incite violence."
The magazine NouvelObs pointed out that if the book were banned, a similar case might be made to ban works by male authors such as Michel Houellebecq for "misogyny".
Martin Page, also a founder of Monstrograph, said: "There's enormous interest in translating this book into English and we've sent the text to a number of publishers who've requested it, in the UK, the US and in Sweden."
Harmange, from Lille, in northern France, describes herself as bisexual, but is married to a man. She said her experience of working with rape victims has made her distrust men she does not know.
Nearly 40 women a day suffer sexual violence in France, she added, whereas women who do not like men "neither kill nor injure anyone, nor prevent them from dressing as they wish, from walking in the street at night, or from expressing themselves as they see fit".
The author said: "I'm simply inviting woman to imagine a new way of being, to take less account of the often ill-grounded opinion of men."
Harmange said she had not expected to sell more than a few hundred copies.
But Monstrograph said it had been overwhelmed by demand after the call for a ban propelled it into the headlines. It is too small to handle further sales, but said a larger publisher would reprint the title.
France has been shaken by the MeToo movement, which has exposed sexism and alleged abuse in its film industry, media and politics.
The Musée d'Orsay in Paris was forced to apologise after refusing entry to a woman on Tuesday because of her plunging neckline. "Rules are rules," a guard reportedly told her.
She wrote to the museum, complaining of "sexist" discrimination. The management immediately apologised for its "overzealous" staff. In a tweet, the museum apologised and said it "deeply regretted the incident".
