A Tesla spokesperson said last month the DOJ requested documents in a "voluntary request" and Tesla has "been cooperative in responding to it". The tweet sent Tesla's share price soaring, but the price collapsed after it emerged that funding had not been secured.
Musk's public antipathy to short-sellers of Tesla - who have sold stock and hope to make a profit by buying it back for less later on - may help the government make the case that he meant to hurt them by claiming funding was secured, said Eric Gordon, a professor at the University of Michigan's Ross School of Business.
Tesla shares dropped in the wake of Tuesday's news and were down almost 6 percent at 12:55 p.m. ET.More news: IPhone XS & XS Max: Unboxing And First Impression
The board has reportedly stepped up its search in recent months for a No. 2 executive to help lift some of the load at Tesla, where the strain of a year that Musk described in a New York Times interview as "excruciating" has more than started to show.
Bloomberg's sources said that the probe is in its early stages, and this comment would seem to back that claim up.
The DoJ investigation deals with the USA attorney's office in the Northern California district.
Shares recovered slightly after their initial drop, and are now down 5.4%, $15.97, at $278.87.More news: Trump orders release of classified documents in Russian Federation investigation
Short-sellers, who bet against the stock appreciating, complained that Musk's announcement was done to manipulate the stock price and cost them money.
"Tesla is bringing most collision repairs in-house, as outside firms take weeks to months for repairs, driving Tesla owners (and us) insane", he said.
The company has been ramping up production of its Model 3 electric vehicle, to such an extent that delivery issues are starting to pop up. Musk later explained in a blog post that the tweet came after a meeting with Saudi Arabian investors that left him feeling that "no other decision makers were needed and that they were eager to proceed".More news: Defiant Serena Williams opens up about US Open controversy
Unlike the Justice Department, the SEC has no power to bring criminal charges. But a person familiar with the investigation said it is a fraud probe seeking to determine whether Musk's statements were meant to mislead investors.