Harry's mother Diana died in 1997 in a auto crash in Paris caused when her driver was speeding to avoid photographers.
Clooney, who was promoting his new television series Catch-22, slammed the invasion of her privacy.
The tense relationship between Meghan Markle and her father Thomas reached new heights in recent days due to the publication of a letter the Duchess of Sussex wrote him that he has since revealed to the press.
I do want to say, I just saw this piece.
Clooney told reporters at a Television Critics Association conference in Pasadena, California that Meghan is "a woman who is seven months pregnant and she has been pursued and vilified and chased in the same way that Diana was and it's history repeating itself".
Britain's famously aggressive press at first welcomed Markle into the royal fold when she and Harry tied the knot at a lavish Windsor Castle wedding last May, in a ceremony attended by Clooney and his human rights lawyer wife Amal.
He added, "We've seen how that ends", alluding to the vehicle accident that claimed the life of the princess in 1997.
The pair's relationship is now at breaking point after Meghan claimed in the letter that Thomas has not contacted her, despite him strongly denying this.
Williams also explains why there's such a big debate about Camilla's future title when Charles becomes king: "There has not been an official notification, and Charles has said in a few interviews, he used the word queen, it's obviously more Charles' expectation and wish that she would be queen, but at the moment the official line is that she'll be princess consort". "She's getting a raw deal there, it's irresponsible". You're taking a letter from a daughter to a father and broadcasting it everywhere. "I'm sort of surprised by that".