A group of shareholders are accusing Musk of failing to tell them he had bought a stake in the company.
On April 4, the CEO of the two companies revealed that he had amassed a 9.2% stake in the company, leading to a surge in the shares.
His disclosure may have been too late.
Federal trade laws require investors to give the SEC 10 days' notice if they take a more than 5% stake in a company.
Musk should have told the SEC by March 24 if he hit this milestone on March 14.
A representative for Musk did not respond to a request for comment.
The lawsuit was filed in New York by the law firm Block and Leviton on behalf of several Twitter shareholders.
Half a dozen legal and securities experts have told The Washington Post that the delay may have helped Musk.
After it was disclosed that Musk had amassed his 9.2% stake, the stock price of the company jumped 27%.
The class action case was filed on behalf of investors who claim they lost out on potential gains if Musk had disclosed his holdings earlier.
What seems clear is that Musk missed the 10-day deadline to report 5% ownership in a public company.
He was given an extra 10 days to buy additional shares before the per share price spike that occurred when he finally announced his holdings.
Musk revealed that he was going to take a seat on the board of the company. He decided not to take the seat because of reasons that have not been announced.