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The SpaceX and Tesla boss tweeted in response to a screenshot posted by the author of the self-published e-book, titled 'Unreported truths about Covid-19 and lockdowns', which showed a message from Amazon's content review department.
The message stated: "Your book does not comply with our guidelines. As a result we are not offering your book for sale."
Replying to the author's tweet, Mr Musk wrote: "This is insane @JeffBezos."
Shortly after, he tweeted: "Time to break up Amazon. Monopolies are wrong!"
The tweets come just two days after he said he was quitting Twitter "for a while".
Amazon has since reversed its decision to block the sale of the 6,400-word book, which questions the reported health risks associated with the Covid-19 coronavirus and criticises government decisions to enforce lockdowns.
The e-commerce giant sent author Alex Berenson an email on Thursday that both the e-book and paperback copies would be sold through the site.
Mr Berenson credited Mr Musk for Amazon's decision to reverse the ban, tweeting: "Thanks to @elonmusk and everyone who helped."
Amazon did not immediately respond to a request for comment but a spokesperson told Reuters that the book had been blocked "in error".
The spokesperson also said that the decision to reverse the ban was not as a result of Mr Musk's tweets.