Prince Harry's fiancee took the decision because the accounts "haven't been used for some time". Ms Markle also ran her own lifestyle website, The Tig, which she closed in April 2017.
The palace said the former actress and UN ambassador was grateful to everyone who had followed her over the years.
The move came after the couple made their first official visit in London.
In December 2017, Ms Markle had 1.9 million people following her posts on Instagram, and more than 350,000 Twitter followers.
Her Facebook page had almost 800,000 likes.
Earlier on Tuesday, Harry and Meghan were greeted by crowds of well-wishers at community radio station Reprezent, in Brixton, which trains youngsters in media skills.
Ms Markle went to the engagement in a Marks & Spencer sweatshirt, Burberry trousers and a Smythe coat.
A DJ at the station, Jeremiah Asiamah, described the pair as a "power couple", and added "they became family in the space of five minutes".
"She's beautiful, such an amazing character, if there's any way you could describe a power couple in this modern day and age, it's definitely them."
The founder of Reprezent FM, Shane Carey, welcomed the visit saying: "We're having the spotlight shone on us from all the world's media."
During the visit Ms Markle picked out male presenter YV Shells, for his work in promoting women on the station.
She said: "Empowering the women to make sure they're in a space where it's not as much [male] driven, to be the man there supporting I think that's incredible."
Harry and Ms Markle also visited Pop Brixton, a community project housing local start-ups and restaurants.
The couple met one of the station's presenters, Gloria Beyi, 17, and her producer Finn Whitehead, 27.
Gloria said there was shock that a such a high-profile couple had visited their radio station: "I think a lot of people thought those two worlds would never collide."
Talking to the teenagers, Ms Markle said: "I can see why your show is so popular. You're so thoughtful and your approach is so engaging."
She added: "I must tune in."