The investors said Musk saved himself $156 million by failing to disclose that he had purchased more than 5% of Twitter by March 14. They asked to be certified as a class and to be awarded an unspecified amount of punitive and compensatory damages.
They also named Twitter as a defendant, arguing the company had an obligation to investigate Musk's conduct, though they are not seeking damages from the firm.
The investors said Musk continued to buy stock after that, and ultimately disclosed in early April that he owned 9.2% of the company, according to the lawsuit, filed on Wednesday in San Francisco federal court.
"By delaying his disclosure of his stake in Twitter, Musk engaged in market manipulation and bought Twitter stock at an artificially low price," said the investors, led by Virginia resident William Heresniak.
Neither Musk nor his lawyer immediately responded to requests for comment. Twitter declined to comment.
The investors said the recent drop in Tesla's stock has put Musk's ability to finance his acquisition of Twitter in "major peril" since he has pledged his shares as collateral to secure the loans he needs to buy the company.
Tesla's shares were trading at around $713 on Thursday afternoon, down from above $1,000 in early April.
The timing of Musk's disclosure of his stake has already triggered an investigation by the U.S. Securities and Exchange Commission (SEC), the Wall Street Journal reported earlier this month.
The SEC requires any investor who buys a stake exceeding 5% in a company to disclose their holdings within 10 days of crossing the threshold.
The investors also said public criticism by Musk of the company, including a May 13 tweet stating the buyout was "temporarily on hold" until Twitter proved that spam bots accounted for less than 5% of its users, amounted to an attempt to further drive the share price down.
Musk on Wednesday pledged an additional $6.25 billion in equity financing to fund his bid for Twitter, a sign he is still working to complete the deal.
Musk was sued earlier this month in Delaware Chancery Court by a Florida pension fund seeking to halt the deal on the basis that some other big Twitter shareholders were supporting the buyout, a violation of Delaware law. Heresniak's lawsuit does not seek to stop the takeover.
(Reporting by Luc Cohen in New York and Tom Hals in Wilmington, Del.; Editing by Noeleen Walder, Nick Zieminski and Matthew Lewis)