The tell-all conversation took place at the couple's home in February - the same day, Prince Philip had been admitted to the hospital as a "precautionary measure". He has since undergone a procedure due to a pre-existing heart condition.
WATCH: Hello! Insider: Harry and Meghan's Oprah Interview
"This morning, I woke up earlier than H, and saw a note from someone on our team in the UK saying that the Duke of Edinburgh had gone to the hospital. But I just picked up the phone and I called the Queen just to check in," the former Suits actress told Oprah.
Prince Harry, 36, then explained that whilst most of his family have a "level of control" in the things they do, he and his wife prefer to just "be authentic".
"For so many in my family, what they do is there's a level of control in that because they're fearful of what the papers are going to say about them," he added. "Whereas with us it was just like, just be yourself. Just be genuine. Just be authentic. If you get it wrong, get it wrong, if you get it right, you get it right."
Prince Harry and Meghan checked in with the Queen
Philip, 99, was admitted to King Edward VII's hospital last month after feeling unwell and has spent almost three weeks there - his longest stay in hospital to date.
During the sensational interview, the couple spoke about a range of topics including Meghan's mental health to accusations the royal family was racist and the full extent of Harry's fractured relationship with his father Prince Charles.
In a lighter moment, Harry and Meghan - who announced in February they were expecting their second child - said they are due to have a baby girl in the summer.
In the US, the show was broadcast on Sunday evening on CBS. In the UK, CBS Presents Oprah with Meghan and Harry will be broadcast on Monday night at 9pm on ITV, and on ITV hub.
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