The suit filed in the US state of Delaware urges the court to order the billionaire to complete his deal to buy Twitter, arguing that no financial damages could repair the damage he has caused.
"Musk's conduct simply confirms that he wants to escape the binding contract he freely signed, and to damage Twitter in the process," the lawsuit contended.
"Twitter has suffered and will continue to suffer irreparable harm as a result of defendants’ breaches."
Twitter shares edged up slightly in after-market trading when the news broke.
Analysts say Musk's attempted exit from the buyout places the company in a vulnerable state at a challenging moment.
After weeks of threats, Musk late last week pulled the plug on the deal, accusing Twitter of "misleading" statements about the number of fake accounts, according to a letter from his lawyers included in a US securities filing.
In his first public remarks since the announcement, Musk took to Twitter over the weekend to troll the company after it said it would sue to enforce the deal.
"They said I couldn't buy Twitter. Then they wouldn't disclose bot info. Now they want to force me to buy Twitter in court. Now they have to disclose bot info in court," he wrote in a tweet, with pictures of Musk laughing with glee.
The termination of the takeover agreement that Musk inked in April sets the stage for a potentially lengthy court battle with Twitter, which initially had opposed a transaction with the unpredictable billionaire entrepreneur.
Twitter has defended its fake account oversight and has vowed to force Musk to complete the deal, which contained a $1 billion breakup fee.
The social network says the number of fake accounts is less than five percent, a figure challenged by Musk who believes the percentage to be much higher.
Musk's norm-defying conduct has come as little surprise to watchers of the Tesla and SpaceX chief after years of statements that flout or test convention and sometimes provoke a crackdown from regulators.
