The actress and women’s right advocate, 52, is one of the 15 inspirational women Meghan chose to be on the cover of the September issue.
Salma says she was in the car when editor-in-chief Edward Enninful called her and told her he was going to put somebody on the phone.
“He told me 'you cannot say the name of the person I'm calling,’” she told CNN.
“Frankly, I thought it was a joke.”
The person turned out to be Meghan, who told Salma that she was working on the project and explained that she was one of her first choices to appear on the cover.
Salma says: “I was like completely shocked. I did not see it coming that way. She started talking about how she's been watching me and why me."
The Mexican-American star says she didn’t even tell her husband Kering CEO François-Henri Pinault, her daughter Valentina Paloma or her publicist.
"I couldn't talk about it and I didn't," she adds.
Salma explained that only she and the photographer Peter Lindbergh knew what the photoshoot was for and the other cover girls “didn’t know that Meghan was how they got there.”
Actor and campaigner Jane Fonda, New Zealand’s prime minister Jacinda Ardern and actor and body positivity advocate Jameela Jamil are also among the women chosen to appear on the September issue of British Vogue, which is available from 2 August.
Other highlights from the magazine include a conversation between Meghan and former First Lady of the United States Michelle Obama and an interview between Prince Harry and primatologist Dr Jane Goodall.