The hashtag '#WeLoveYouMeghan' has since become a trending topic on Twitter.
The clip comes days after her husband Prince Harry broke down during an emotional speech at the WellChild awards on Tuesday night.
The Duke of Sussex was talking about becoming a father with Meghan when he appeared to be holding back tears, with host Gaby Roslin giving him a comforting pat on the back.
"They never fail to inspire me - but this year it resonates in a different way because now I'm a father. Last year when my wife and I attended we knew that we were expecting our first child, no one else knew, but we did," Harry said, recalling how he knew Meghan was pregnant with his son Archie at last year's WellChild Awards.
"I remember squeezing Meghan's hand so tight during the awards and both of us thinking what it would be like to be parents one day and more so would it would be like to protect and help our child should they be born with immediate challenges or become unwell over time," he continued.
Prince Harry opened up about being a parent to baby Archie and how meeting the WellChild kids and parents gave him a sense of "hope."
"And now talking to all of you as parent pulls at my heart strings, in a way I never could have understood, until I had a child of my own. No parent wants to hear that their child will suffer, that they will face extraordinary challenges - that will affect them throughout their lives," he said, before adding:
"After meeting all the WellChild kids and parents over the years you have managed to give us a sense of optimism, of hope and of strength that no professional, no best selling book or advice could ever give us - so thank you for being you."
WATCH: Prince Harry breaks down during speech