The Justice Department asked Tesla for documents about Musk's announcement, Tesla said, describing it as a "voluntary request." The company said it was co-operating and that the matter "should be quickly resolved."
The probe by the Justice Department, which can press criminal charges, comes on top of a civil probe by the Securities and Exchange Commission and shareholder lawsuits.
Musk surprised investors on Aug. 7 with his plan to take Tesla private, tweeting that he had "funding secured" for a deal that would have valued the company at $72 billion.
After two weeks, Musk abandoned the plan, saying it would be even more time-consuming and distracting than anticipated, and that "most of Tesla's existing shareholders believe we are better off as a public company."
Tesla's stock, which has lost about 25 percent since its gains after Musk first tweeted about going private, fell 3.5 percent to $284.50 on Tuesday.
To charge Musk with a crime, the Justice Department would need to show that he intended to manipulate Tesla's stock price.
For a civil enforcement action, the SEC would only need to show that Musk acted negligently, which is easier to prove.