The pair married in 2010 and have three children, daughters Olive, 17, and Elula, 13, and a nine-year-old son Montgomery.
It comes days after the Australian actress Rebel Wilson made a series of allegations about Baron Cohen in her memoir, Rebel Rising, which was released in the US earlier this week.
Wilson claimed that she felt as if the British comedy star “sexually harassed” her on the set of the film Grimsby, a spy action comedy released in 2016 and titled The Brothers Grimsby in the US, in which she played his on-screen girlfriend.
She had previously released a statement saying she had “worked with a massive a–hole” and vowed that she “will not be bullied or silenced with high-priced lawyers or PR crisis managers” from editing out the claims from her book.
Baron Cohen denied the claims as “demonstrably false”. His spokesman said: “While we appreciate the importance of speaking out, these demonstrably false claims are directly contradicted by extensive detailed evidence, including contemporaneous documents, film footage, and eyewitness accounts from those present before, during and after the production of The Brothers Grimsby.”