The couple made a visit to the UN General Assembly in September 2021 but didn't participate in the speeches at the assembly hall.
Nelson Mandela Day has been celebrated by the UN since 2009 and the public are urged to participate by making a difference in their community.
A post on the United Nations website states: "Everyone has the ability and the responsibility to change the world for the better! Mandela Day is an occasion for all to take action and inspire change."
This year's Nelson Mandela Day tagline is, 'Do what you can, with what you have, where you are.'
In 2019, Harry and Meghan - who have children Archie, three, and Lili, 13 months, together - met Mandela's widow, Graca Machel, during a visit to South Africa and are believed to have wanted to honour the late activist since then.
Machel said to the couple during their meeting: "It's wonderful meeting you. I'm sure we're going to be working together in the future. I can feel the vibe."
During the trip, the couple also met Mandela's granddaughter, Zamaswazi Dlamini-Mandela and his former cellmate Andrew Mlangeni.