"Just setting up my twttr," the post, sent from Mr Dorsey's account in March 2006, reads.
It will be sold as a non-fungible token (NFT) - a unique digital certificate that states who owns a photo, video or other form of online media.
But the post will remain publicly available on Twitter even after it has been auctioned off.
The buyer will receive a certificate, digitally signed and verified by Mr Dorsey, as well as the metadata of the original tweet. The data will include information such as the time the tweet was posted and its text contents.
Most of this information, however, is already publicly available.
The tweet was listed for sale on 'Valuables by Cent' - a tweets marketplace that was launched three months ago.
In a post on the site, the platform's founders compare the buying of a tweet to that of a more traditional autograph or piece of memorabilia.
"Owning any digital content can be a financial investment," it says. "[It can] hold sentimental value. Like an autograph on a baseball card, the NFT itself is the creator's autograph on the content, making it scarce, unique, and valuable."
Tweets are the latest digital assets to be monetised through so-called non-fungible tokens.
NFTs use the blockchain, the same distributed database technology underlying Bitcoin and other cryptocurrencies, to create unique certificates of ownership of any kind of digital goods.
While the idea that digital artists can earn an income by offering buyers some sense of ownership has its attractions, the "sale" of tweets will leave many scratching their heads.
Valuables, the platform marketing Mr Dorsey's tweet, seems to recognise that the concept will leave people bemused. In its FAQ it explains "owning any digital content can... hold sentimental value and create a relationship between collector and creator".
Most of us might think that this is a high price to pay for a relationship with the Twitter boss. But given the feverish and often irrational state of any kind of cryptocurrency related market, maybe the buyer is betting there'll be someone along soon to take the tweet off their hands at an even higher price.
Meanwhile, on the basis that if you can't beat them, join them, I put one of my tweets up for sale. It was about this story - and I've just accepted a bid of $1. That might sound modest but seeing as I've got 72,466 other tweets available it could be the start of something big….
Old offers for Mr Dorsey's tweet suggest that it was first put up for sale in December, but the listing gained more attention after he tweeted a link to it on Friday. That tweet has since been shared thousands of times.
Within minutes of the tweet being posted, bids reached more than $88,000.
But they skyrocketed on Saturday, with a bid of $1.5m being usurped by a $2m offer at around 15:30 GMT.
According to Valuables by Cent's terms, 95% of a tweet's sale will go to the original creator with the remainder going to the website.