The lawsuit said Musk became an “interested stockholder” after taking a more than 9 per cent Twitter stake, requiring the delay.
Musk also runs electric car company Tesla and is the world’s richest person according to Forbes magazine.
Twitter and its board, including Chief Executive Parag Agrawal, are also defendants.
The lawsuit seeks to delay the merger’s closing until at least 2025, declare that Twitter directors breached their fiduciary duties, and recoup legal fees and costs.
Twitter declined to comment. A lawyer for Musk did not immediately respond to a request for comment.