"She's 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," Clooney told reporters on Tuesday.
He added a stark warning: "We've seen how that ends."
Diana, Meghan's late mother-in-law, endured scrutiny from the media around the world before, during and after her marriage to Prince Charles. She died in a car crash in 1997 when her car was "being pursued at high speeds by photographers on motorbikes," the BBC reported.
Clooney and wife Amal Clooney were guests at Meghan and Prince Harry's wedding ceremony in May. He made his comments while promoting his new Hulu series "Catch-22" at the Television Critics Association conference in California.
The actor's comments come two days after Meghan's dad shared a handwritten letter from his daughter with the press. In the five-page letter, she implored her father, Thomas Markle, to "stop creating so much pain."
When asked by a reporter why he released the private message, Thomas said, "I love my daughter very much. I'm very sad."