Mr Isaacs and the second plaintiff, William Chamberlain, have alleged that Tesla's stock price was artificially inflated and federal securities laws had been breached.
Musk, often the center of controversy, did not prove he had the funds to finance the operation - despite tweeting "funding secured".
Musk announced on Twitter earlier this week that he was considering taking the electric carmaker private at a share price of $420 (£328.86) and total market value of $72bn, adding that he had already secured the necessary funding. The company is based in nearby Palo Alto, California. The remark set off a frenzy of trading in Tesla shares, even as investors were struggling to discern whether the tweet was legitimate and what precisely it meant.
Short-sellers borrow shares they believe are overpriced, sell them, and then repurchase shares later at what they hope will be a lower price to make a profit.More news: Family of man who stole and crashed plane 'shocked and devastated'
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The stock has since given back more than two-thirds of that gain, in part following reports that the U.S. Securities and Exchange Commission had begun inquiring about Musk's activity.
The complaint said the class period begins on the afternoon of August 7, when the defendants launched their "nuclear attack" on short-sellers, and ends the next day.
Short-sellers of Tesla's stock have faced increasing aggression from Musk over recent months, with the billionaire citing the lack of market support as one of the main reasons he wants to take the company private.
One of the lawsuits, filed by shareholder Kalman Isaacs, seeks class action status on behalf of investors who bought Tesla stock on August 7 and August 8.
The cases are Isaacs v Musk et al, U.S. District Court, Northern District of California, No. 18-04865; and Chamberlain v Tesla Inc et al in the same court, No. 18-04876.