The SpaceX and Tesla founder made the comments on Thursday after author Alex Berenson tweeted a screenshot from Amazon Kindle telling him that his book about coronavirus did not meet its guidelines.
Mr Musk tagged Amazon chief executive Jeff Bezos in a tweet, saying the decision was "insane".
He added: "Time to break up Amazon. Monopolies are wrong!"
Earlier this week, Mr Musk announced he was taking a break from social media, despite being one of the platform’s most prolific, high-profile users.
Time to break up Amazon. Monopolies are wrong!— Elon Musk (@elonmusk)June 4, 2020
He said he would be “off Twitter for a while” in a post in the early hours of Tuesday morning.
But he returned on Thursday, responding directly to the former New York Times reporter and calling for Amazon to take action.
Yesterday @amazon tried to censor “Unreported Truths,” claiming it did “not comply with our guidelines.” You made Amazon back down - and as of now both the Kindle and physical editions are #2 on Amazon. YOU HAVE SPOKEN FOR THE TRUTH - and I am so grateful you did. Thank you. pic.twitter.com/Vw3XC8vpQu— Alex Berenson (@AlexBerenson)June 5, 2020
"They censored it!" Mr Berenson tweeted, referring to his book 'Unreported Truths'.
"It is based entirely on published government data and scientific papers. It doesn't say coronavirus isn't real or doesn't kill people."
Mr Berenson told Fox News that Amazon contacted him shortly after Mr Musk spoke out about the "censorship" and agreed the publish the book.
Amazon said it was an “error” and the book shouldn’t have been removed.
Mr Musk recently celebrated a major milestone, as SpaceX became the first private company to send humans into orbit, carrying Nasa astronauts Robert Behnken and Douglas Hurley to the International Space Station (ISS) over the weekend.
The launch was also the first time Nasa had launched astronauts from US soil in nine years.
The billionaire has had a number of controversial moments using his Twitter account.
Last year he was found not liable in a defamation case involving a British cave explorer.
Vernon Unsworth had sued Mr Musk after he called him “pedo guy” and “sus” (suspicious) on Twitter in a spat following the July 2018 Thai cave rescue.
Mr Musk has also previously been sanctioned by the US Securities and Exchange Commission (SEC) over allegations of misleading investors with some of his tweets, including one about taking the company private.
He has said in the past that his Twitter account is “complete nonsense”.
The South Africa-born entrepreneur and his partner, Canadian singer Grimes, made headlines last month when they welcomed their first child together, a boy, giving him the unusual name X Æ A-Xii.