Clooney, who is friends with Meghan and her husband Prince Harry, defended the Duchess after Britain's Mail on Sunday newspaper published a personal letter allegedly sent by Meghan to her estranged father.
"They're just chasing Meghan Markle everywhere, she's been pursued and vilified," Clooney said at a promotional event for his new film, according to the UK's Press Association (PA) news agency. "I can't tell you how frustrating it is to see that."
"She's a woman who is seven months pregnant and she is being pursued and vilified and chased in the same way that Diana was, and it's history repeating itself. And we've seen how that ends," Clooney added, according to PA.
Kensington Palace has not yet responded to CNN's request for comment.
Meghan has also faced intense interest from the unsparing UK press since her engagement to Prince Harry was announced in 2017.
Clooney, who attended Meghan and Harry's wedding last year alongside his wife, the human rights lawyer Amal Clooney, said he had seen the recent coverage about the Duchess's supposed letter.
"You're taking a letter from a daughter to a father and broadcasting it everywhere," he said, according to PA. "She's getting a raw deal there, it's irresponsible. I'm sort of surprised by that."
The letter received widespread coverage in Britain, with The Mirror newspaper consulting a handwriting expert to claim that the Duchess's writing reveals her to be "emotionally insecure and self-pitying."
Previous sensationalist headlines in British tabloids since Meghan's marriage to Harry have focused on her alleged "tantrums" and her "tit-for-tat war" with Catherine.