Tesla later admitted that it did not have the funding for the deal, and less than three weeks after his tweet, Musk walked back the prospect of going private.
Tesla shares soared last month on the privatization news, up 6 percent from prior to the initial tweet, and closed up 10.98 percent from the previous day.
"Musk made his false and misleading public statements about taking Tesla private using his mobile phone in the middle of the active trading day", the SEC said in the complaint.
Thursday's lawsuit makes Musk one of the highest-profile executives to be accused by the SEC of securities fraud.More news: Murray reaches 2nd round of Shenzhen Open as Zhang retires
Grundfest said that whether Musk can stay on as CEO is "almost entirely up to Elon" and whether he is able to negotiate a settlement with the SEC.
The SEC's charges pose a potentially devastating threat to Musk's future as an entrepreneur, as the agency is seeking fines and the return of ill-gotten gains, as well as potentially barring him from ever serving as an officer or board member of a publicly-traded company.
From the SEC's suit: "Musk's statements, disseminated via Twitter, falsely indicated that, should he so choose, it was virtually certain that he could take Tesla private at a purchase price that reflected a substantial premium over Tesla stock's then-current share price, that funding for this multi-billion dollar transaction had been secured, and that the only contingency was a shareholder vote".
"This unjustified action by the SEC leaves me deeply saddened and disappointed", Musk said in an emailed statement. "Integrity is the most important value in my life and the facts will show I never compromised this in any way". Both the SEC and Tesla have not yet responded to requests for comment. As evidence, the complaint notes that within minutes of the first tweet, the head of investor relations at Tesla texted Musk asking if the tweet was legitimate.More news: European Union trade chief defends Freeland after Trump trash-talks 'Canada's negotiator'
The Securities and Exchange Commission has opened a case against Tesla and SpaceX CEO Elon Musk.
Nasdaq, which requires advance notice of market-moving information, suspended trading for 90 minutes after the tweet, having received no advance notice of the announcement.
Shares of Tesla are swapping hands at right around $310 this morning.More news: Tesla CEO Elon Musk's latest insane scheme to meet production targets