The BBC has been unable to verify the post was written by Mr Musk himself, but it has pushed the shares 6% higher.
Musk tweeted that he hoped all current investors would remain were the company to go private.
The disclosure initially raised questions whether the eccentric Musk was joking, but he then amplified on his plan in a subsequent tweet that said he meant to create a special fund that would allow all current Tesla shareholders to retain a stake in the auto maker if they want. In the future, once Tesla enters a phase of slower, more predictable growth, it will likely make sense to return to the public markets. And if the information in the tweet isn't true, Musk could be looking at some stock price manipulation allegations.
Nasdaq stock exchange halted trading in Tesla shares around 2.08pm local time.
The Tesla CEO said shareholders can either remain as investors in a privately-held version of the company or agree to a buyout at $420 per share. Musk owns almost 20pc of the company.
Starting in November, Tesla faces repayment of $1.7 billion in debt over the next 18 months that is tied to the company's stock price. It followed the news that Saudi Arabia's sovereign wealth fund had built a less than 5 percent stake in Tesla worth about $2 billion.
After rising as much as 8.5 percent, the company's shares gave up some of their gains.
Tesla has not confirmed whether the tweet was real - or if the CEO's account was hacked. I wanted to let you know my rationale for this, and why I think this is the best path forward.
Elon Musk is the world's 31st-richest person and Tesla's largest shareholder.
With shares at $369.90, short-sellers logged an on-paper loss of $977 million, according to financial analytics firm S3 partners.
Munster also said he did not see legal risk from Musk's tweets due to the Reed Hastings Rule, an SEC guideline announced in 2013 that said it was OK for companies to reveal key information on social media as long as investors have been alerted.
George Galliers of Evercore ISI said he believed the tweet was serious.
I fundamentally believe that we are at our best when everyone is focused on executing, when we can remain focused on our long-term mission, and when there are not perverse incentives for people to try to harm what we're all trying to achieve.