Business reporter.
The investors are accusing Musk and the social media platform of botching the deal to take the company private.
He is accused of violating California corporate laws in a number of ways.
It accuses the boss of the electric car maker of "wrongful conduct", as his "false statements and market manipulation have created chaos" at the company's headquarters in San Francisco.
The offer price for Mr Musk is around $54.20.
The lawsuit said that Mr Musk benefited financially by delaying the disclosure of his stake in the company and by his plan to become a board member.
It claimed that several of Mr Musk's posts were misleading.
Mr Musk said his takeover bid for the social media firm was on hold because of his doubts over the number of fake accounts on the platform.
The lawsuit said that he knew about the fake accounts and that he tried to manipulate the market for Twitter shares.
It said that Mr Musk doubled down on his allegations four days later, when he said that the deal couldn't go forward.
The lawsuit was filed as Mr Musk continued to malign the company he wants to buy for $44 billion in an effort to renegotiate the purchase price, according to Frank Bottini, one of the lawyers representing the investors.
The complaint we filed in San Francisco seeks to hold Musk liable for his conduct.
Analysts think Mr Musk may be looking for ways to lower his offer or walk away from the deal.
He's concerned about the number of fake accounts on the social media site.
A bot is a software programme that sends out automated posts and is often associated with misinformation on social media platforms.
Mr Musk said that he may try to pay less for the company than the board agreed to in March.
Speaking at a technology conference earlier this month, he said striking a deal at a lower price was not out of the question.
The proposed class-action lawsuit was filed this week at the US District Court for the Northern District of California by investor William Heresniak, who said he was acting on behalf of himself and all others similarly situated.
A class-action is a lawsuit that has been filed by a group of people.
The lawyers for Mr Musk did not respond to the request for comment on Friday.
When contacted by the BBC, it was not possible to say anything.
The company confirmed earlier this month that two of its bosses who had been leading its consumer and revenue operations were leaving.
Most hiring has been paused except for business critical roles.
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