The comic conducted a spoof interview with former US Senate candidate Roy Moore in the guise of Israeli anti-terrorism expert Erran Morad. Cohen tweeted ahead of the show's finale last month. It's been a long time since I fought for my country in Vietnam.
In the show broadcast in the USA in July, when the beep sounds, Mr Moore tells Baron Cohen: "I support Israel".
Once Cohen sits down with Moore, he begins to tell the former Chief Justice of the Supreme Court of Alabama about a new technology that Israel has developed to "identify other abnormalities".
During the segment, Cohen brought in a supposed "paedophile detector" device. The wand beeps when it waves over Moore.
Sacha Baron Cohen attends the Vanity Fair Oscar Party in Beverly Hills, Calif., March 4, 2018. The machine beeped only when close to the politician.
"I've been married for 33 years and never had an accusation of such things", Moore said.More news: Airstrike near United States base in southeastern Syria kills 8 pro-Assad fighters
"If this is an instrument", he continues, "certainly, I'm not a pedophile".
A release form signed by Moore for his appearance on the program, the complaint continues, was invalid due to the supposedly fraudulent conditions under which it was signed.
He is represented by Larry Klayman, the founder of Judicial Watch and Freedom Watch.
Mr Klayman said Mr Moore thought he was receiving an award for supporting Israel when he agreed to appear on the show. He believed that he was invited on Yerushalayim TV, a made up Israeli TV series.
The lawsuit said Baron Cohen's show mocked him with a "false and fraudulent portrayal" that harmed Moore's reputation and caused "severe emotional distress" to his family.More news: Fuel prices to remain unchanged: Radebe
Moore is suing for damages of $95 million and has asked for as a jury trial.
Showtime issued the following statement: "The press has been sent copies of an alleged complaint, yet to our knowledge SHOWTIME has not been served".
Now Mooer is claiming $95million (£73million) in damages from Baron Cohen and the CBS-owned Showtime network which aired the show in the US. " on the Showtime cable channel, which is part of the CBS Corporation".
Former Alaska Gov. Sarah Palin also appeared on the show, slamming the prank in which Cohen appeared as a disabled USA veteran in a wheelchair as "evil" and "sick".
In the court documents filed in Washington DC, former Alabama Senate candidate Moore alleges the release form he signed before appearing on the show is null and void because it was signed under false pretences.More news: Federer, Djokovic and Sharapova in action at U.S. Open