Elon Musk is providing financial support for the case, in which he publicly invited people to participate via his platform X.
Ms Carano is seeking $75,000 (£60,000) in compensation and is asking the court to compel Lucasfilm to replace her with another actor.
Spokespersons for the defendants were not promptly accessible for commentary.
Carano, aged 41, a former MMA fighter, played the character of Cara Dune in the first two seasons of the Disney+ series The Mandalorian.
She routinely engaged in online conflicts with individuals with left-wing political views during that period.
However, detractors called for her dismissal after her February 2021 Instagram post, in which she drew a parallel between the persecution of Jews by the Nazis and the current political environment faced by Republicans.
"Due to the editing of history, many individuals in contemporary society are unaware that the government, prior to enabling Nazi soldiers to effortlessly gather thousands of Jews, instigated animosity among their own citizens solely based on their Jewish identity," said the article.
"What distinguishes this from harbouring animosity towards someone based on their political perspectives?"
On the same day, MsLucasfilm, the production company responsible for the programme, and UTA, the talent agency that had been her representative for over two years, terminated Ms. Carano.
A spokesman from Lucasfilm said that the individual's social media remarks, which belittle others based on their cultural and religious backgrounds, are both repugnant and not permissible.
UTA is not mentioned in the court petition from Tuesday, which asserts that the Walt Disney Company is responsible for the agency's decision to terminate her.
The 59-page legal action, submitted to the California federal court, presents claims of unjust dismissal and reprisal in a detailed account filled with allusions to the Star Wars franchise.
The complaint starts by stating that Defendants recently established a strict regime in which only one set of beliefs, manner of expression, or behaviour is deemed acceptable, and anybody who dared to challenge or did not completely conform to this regime would not be tolerated.
Ms Carano alleges that she was terminated due to her audacity in expressing her views and resisting the online collective of bullies who insisted on her conformity to their radical progressive ideology.
The complaint claims that the actress was subjected to disparate treatment compared to two male co-stars, who engaged in the act of writing or sharing internet articles that defamed Republicans as Nazis but suffered no repercussions.
Ms. Carano issued a comprehensive statement about X, expressing that she had been targeted by a concerted effort to intimidate, ruin, and use her as a cautionary tale.
"As American citizens, artists do not relinquish our rights when we become employed," she remarked, expressing gratitude towards Mr. Musk and her supporters.
The billionaire expressed her intention: "Kindly inform us if you are interested in participating in the legal action against Disney."
Mr Elon Musk has pledged to provide financial assistance to those who encounter prejudice due to their contributions to X.
The company's representative supported Ms. Carano's case, stating that it aligns with their dedication to free expression.
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