It comes after images of Meghan were published in the media showing her taking a stroll through a public park on Vancouver Island.
The duchess can be seen smiling as she walks along with Archie and her two dogs.
Lawyers for the couple claim these were taken without her consent – and that the photographer was hiding in the bushes and spying on her.
They also claim there were previous attempts to photograph them inside their home using long range lenses and that paparazzi were permanently camped outside their home.
This comes days after Harry and Meghan agreed a deal to step away from the Royal Family.
In a speech at a dinner for supporters of his Sentebale charity, the prince said the decision was made as they wanted to lead a more “peaceful life”.
“The decision that I have made for my wife and I to step back, is not one I made lightly. It was so many months of talks after so many years of challenges.
“And I know I haven’t always gotten it right, but as far as this goes, there really was no other option.”
Harry and Meghan’s lawyers also highlighted serious safety concerns about how the paparazzi had been driving in Canada.
Prince Harry’s mum, Diana, died on 31 August 1997 after the car she was in crashed into a concrete pillar in a Paris tunnel, whilst trying to flee paparazzi photographers.
Harry referenced this in his speech on Sunday, adding: “When I lost my mum 23 years ago, you took me under your wing. You’ve looked out for me for so long, but the media is a powerful force, and my hope is one day our collective support for each other can be more powerful because this is so much bigger than just us.”
Sky’s royal correspondent Rhiannon Mills said: “We’ve heard statements previously but this is the first time in his words that he’s told an audience how he’s feeling.
“He is reiterating the fact that Harry and Meghan have wanted this new kind of life partly because of the intense scrutiny that they feel they faced from the press here in the UK but also around the world.
“After all we also heard from the Queen how she recognised that intense scrutiny that they’ve faced when it came to coming up with that deal to allow them to live that more independent life.”