The 71-year-old was accused by nine women of sexual misconduct during his unsuccessful bid to win one of Alabama's two Senate seats last November. Moore denied the allegations throughout the race.
Larry Klayman, founder of the conservative group Freedom Watch, is representing Mr Moore and his wife Kayla in the lawsuit.
"Sasha Baron Cohen, who is not only low class but also a fraudster, will now, along with Showtime and CBS, be held accountable for his outrageous and false, fraudulent and defamatory conduct which callously did great emotional and other damage to his great man and his wife and family", Klayman said in a statement.
Cohen invited former U.S. Senate candidate from Alabama Roy Moore under the pretense of granting him an award for his support for Israel, but he used the opportunity to mock and embarrass the Republican.
CBS and Showtime did not immediately respond to requests for comment on behalf of the defendants.
The show begins as Cohen, in full transformative makeup, discusses the importance of technology in the military.
As is generally the case with Cohen's victims, Moore signed a release before the taping took place.
"Defendant Cohen and his agents including defendants Showtime and CBS knowingly made this false material representation to fraudulently induce Judge Moore to appear on the program, with Mrs. Moore present, where Defendant Cohen and defendants Showtime and CBS would falsely portray, mock and defame Judge Moore as a pedophile".
The wand device remained silent as Cohen passed it over himself, but it beeped after he passed it over Moore several times.
The filing demands a jury trial and seeks damages in excess of $95 million "and any other relief that this court may deem just".
Baron Cohen has faced past lawsuits over similar pranks, but those actions faltered because the individuals had signed releases.
After Moore discovered the truth, his attorney sent warnings to Cohen, Showtime and CBS that he would "resort to appropriate legal remedies if they chose to air the segment", according to the complaint. The suit alleges that the release was obtained on fraudulent grounds. The interview has already seen the light of TVs and, as of this writing, is still up on YouTube.