In a sketch for his series Who Is America?, Baron Cohen pretends to be an Israeli anti-terrorism expert demonstrating a “paedophile detector”.
When the “device” is waved near Mr Moore, it beeps.
In last year’s Senate campaign, Mr Moore was dogged by allegations of sexual misconduct, which he denies.
His lawyers say the satirist falsely accused their client of being a sex offender. They are seeking $95m (£73m) in damages from Baron Cohen and from the Showtime and CBS networks.
Representatives for Baron Cohen have not responded to the lawsuit, filed in a federal court in Washington. A spokeswoman for Showtime said it did not comment on pending litigation.
Mr Moore, 71, stood as a Republican candidate in last year’s Senate race in his home state of Alabama, but lost to Democratic opponent Doug Jones.
He had been expected to win in the conservative state, but his campaign was dogged by allegations of sexual misconduct with teenagers. He denies any wrongdoing.
In May, Mr Moore filed a defamation lawsuit against women who made allegations against him, saying they were part of a “political conspiracy” to undermine his campaign.
Mr Moore said he had travelled to Washington to appear on what he thought was an Israeli TV show in the belief that he was to receive an award for his pro-Israel…