The National Enquirer published a story last month that included lurid texts between Bezos and former TV anchor Lauren Sanchez.
Mr Bezos, who is worth $150 billion (£115 billion), said that he was told by representatives of David Pecker, chairman of American Media Inc (AMI), owner of the Enquirer, to stop his investigation or else the publisher would print a series of explicit photographs of Mr Bezos, 55, and Ms Sánchez, 49.
Bezos declined to do so.
However, in the interests of expediating this situation, and with The Washington Post poised to publish unsubstantiated rumors of The National Enquirer's initial report, I wanted to describe to you the photos obtained during our newsgathering.
So, in an attempt to out the publication today, Jeff published their alleged threat via a "confidential" email sent to Martin Singer, the litigation counselor for his investigator. "I hope common sense can prevail - and quickly".
"Of course I don't want personal photos published, but I also won't participate in their well-known practice of blackmail, political favors, political attacks, and corruption", Bezos wrote of AMI, in explaining his decision to go public. If in my position I can't stand up to this kind of extortion, how many people can?
The blog post is the latest twist in a weeks-long saga that has brought the personal life of Bezos, the richest person in the world, into the spotlight.
A spokesman for the US attorney's office in Manhattan did not immediately comment on Bezos' assertion that AMI had committed extortion.
Mr Bezos said his ownership of the Washington Post was a "complexifier" for him because he had made enemies of "certain powerful people", including President Donald Trump, who is a friend of AMI's boss David Pecker.
The alleged extortion raises questions among some legal observers about whether AMI and its chief executive David Pecker have violated a cooperation agreement AMI made previous year with federal prosecutors in connection with a $150,000 hush-money payment given to Karen McDougal, the Playboy model who claims she had an affair with President Donald Trump.
Pecker is now cooperating with federal investigators who are looking into the company's involvement with the Trump campaign.
In its January 9 story, the Enquirer said reporters followed Bezos and Sanchez "across five states and 40,000 miles" and "tailed them in private jets, swanky limos, helicopter rides, romantic hikes, five-star hotel hideaways, intimate dinner dates and "quality time" in hidden love nests".
Sounds like soon some people at The National Enquirer are going to "learn to code".
· Mr. Bezos face selfie at what appears to be a business meeting. As chairman of American Media Inc., Pecker played a part in making the payments to former porn star Stormy Daniels and former Playboy model Karen McDougal, both of which prosecutors believe may have violated campaign finance law, according to The New York Times.