By Agence France-Presse
Shares finished down 2.6 percent at $338.69 after news of the formal demand for information was published by Fox Business and The New York Times. Shares fell as much as 4.5 percent earlier in the session.
The development suggests the oversight by the US Securities and Exchange Commission -- which was characterized in previous news articles as an inquiry -- has "advanced to a more formal, serious stage," said The Times, which cited a person familiar with the matter.
A subpoena "typically requires the approval of top SEC officials," the newspaper added.
A Wall Street Journal story published after the stock market closed said the subpoena sought information from each of Tesla's directors.
A Tesla spokesperson declined comment.
Musk has been under scrutiny after disclosing a proposal to take the company private on Twitter and saying that financing for a transaction was "secured," a claim that analysts viewed skeptically and has looked shaky based on several news accounts.
Some Tesla board members were reportedly caught off guard by Musk's tweets and have urged the controversial chief executive to stop using the social media platform.
Tesla's board of directors said Tuesday it had formed a special committee to consider the proposal.
Musk on Monday explained in a blog post that his statements about financing were based on his conversations with Saudi Arabia's sovereign wealth fund and other investors.