The BBC has been unable to verify the post was written by Mr Musk himself, but it has pushed the shares 6% higher.
On Twitter Tuesday, Musk said he has secured funding from a private buyer.
"I'm trying to accomplish an outcome where Tesla can operate at its best, free from as much distraction and short-term thinking as possible, and where there is as little change for all of our investors, including all of our employees, as possible", Musk said.
Tesla did not immediately respond to a request for clarification.
Musk has occasionally griped about the frustrations of running a public company: past year he called Tesla a "drama magnet" - and he has vowed not to do an initial public offering for his other major venture, SpaceX, until after regular trips to Mars begin, if ever.
"Our guess is there is a one-in-three chance he can actually pull this off and bring Tesla private", Munster said.
And yet it also left many questions unanswered, namely how Musk - who owns nearly 20 percent of the company - would be able to come up with the $66 billion necessary to complete the transaction. His asking price of $420 would be 22 percent of Monday's closing share price, and almost 9 percent above the stock's all-time closing high of $385.
California's Carr Fire Was Bad. The Mendocino Complex Fire Is Worse
Forest Service reported that the fire crossed a highway Sunday evening, forcing crews to retreat from the fire's edge. Meanwhile, firefighters are battling more than a dozen other major fires amid California's hot and dry weather.
Rick Gates Testifies Against Former Mentor Paul Manafort in Special Counsel Trial
Those admissions are likely to become a focal point for Manafort's defence team when he is cross examined on Tuesday. Some of the manoeuvrers were at the request of Mr Gates, while others implicated Mr Manafort, Ms Laporta testified.
'I thought it was a doll': Baby found floating in river dies
The body of a baby boy was recovered in New York City yesterday close to one of the city's most famous landmarks. The baby, later determined to be about 8 months old, was rushed to the hospital, where he was pronounced dead.
Last month, Musk attacked British diver Vern Unsworth, who had dismissed the Tesla chief's efforts to help the rescue mission for the 12 boys as a "PR stunt" in a widely seen interview on CNN.
Second, my intention is for all Tesla employees to remain shareholders of the company, just as is the case at SpaceX.
"The market doesn't believe him", said David Kudla, the CEO of Mainstay Capital Management, which is betting against Tesla.
But asked if he would take legal action against Musk over the allegation, Unsworth said: 'If it's what I think it is yes'.
The US Securities and Exchange Commission (SEC) allows companies to use social media outlets like Facebook and Twitter to announce key information in compliance with its "fair disclosure" rules, as long as investors are alerted about which social media outlets will be used to disclose such information.
With shares at $369.90, short-sellers logged an on-paper loss of $977 million, according to financial analytics firm S3 partners.
The stock had climbed slightly earlier in the day after the Financial Times reported that Saudi Arabia has quietly built a big stake in Tesla.
George Galliers, analyst at Evercore ISI said he believed the tweet was serious.