That said, if they do want out, they can sell their shares at $420 per share, which is a fair bit higher than Tesla's current stock price ($382.67 at the time of writing, up from today's open price of $343.84).
It's unclear from where Musk has secured funding.
Tesla did not return repeated calls for comment from CNBC, nor did the Securities and Exchange Commission, as of this publishing. On April Fools' Day, amid growing concerns about the company's cash stockpile, Musk joked via tweets that Tesla had gone "so bankrupt you can't believe it".
In a second tweet on Tuesday, Mr Musk said taking the company private would not lead to a single dominant shareholder.
The stock since settled at $366.94 before exchanges halted trading, pending an upcoming announcement from the company.
Shares were pummeled in May after Musk abruptly cut off questions from Wall Street analysts over Tesla's spending plans.
On the social media platform he noted the possibility of taking Tesla - a publicly traded company since 2010 - private.
He also said that he would hold on to his almost 20% stake in the company if it were taken private, and that he wouldn't expect himself or any other investor to have a controlling vote after the buyout.
The stock had already been heading upwards after news about a Saudi Arabian fund with a large (about 3 to 5 percent) stake in the electric auto company. If Musk can't prove the allegedly secured funding at $420 per share, he may be accused of market manipulation or market fraud.
The announcement, made initially via Twitter, stunned investors and sent Tesla's stock price soaring as much as 13 percent.
Tesla has not confirmed whether the tweet was real - or if the CEO's account was hacked.
In a 2013 report, the SEC said companies can use social media outlets to announce important information, so long as they comply with regulations and "investors have been alerted about which social media will be used to disseminate such information". I wanted to let you know my rationale for this, and why I think this is the best path forward.
"I can't believe this is something to bluff or make fun of", said George Galliers of Evercore ISI.
"The reason for doing this is all about creating the environment for Tesla to operate best", Musk began.