The couple have asked that anyone who wants to send them a present to mark their wedding next month make a donation to charity instead, Prince Harry's office said on Monday.
Harry and U.S. actress Markle, who will marry at Windsor Castle on May 19, have drawn large cheering crowds whenever they have appeared in public since their engagement was announced last November.
In a statement, Harry's office said the couple were incredibly grateful for he goodwill they had been shown and "are keen that as many people as possible benefit from this generosity of spirit"."
The couple have therefore asked that anyone who might wish to mark the occasion considers making a donation to charity, rather than sending a wedding gift," the statement said.
Harry and Markle have selected seven charities, none of which they have direct links to, which they want people to support.
These include the Children's HIV Association, the Myna Mahila Foundation which helps women in Mumbai's slums, the Crisis homelessness charity, conservation group Surfers Against Sewage and Scotty's Little Soldiers, which supports children who have lost a parent while serving in the British military.
"To have been personally chosen by Prince Harry and Meghan Markle is an incredible honour for Scotty's Little Soldiers and we are extremely grateful for the opportunity," said the charity's founder Nikki Scott.
"Having met Prince Harry at Buckingham Palace last year, I know that the Armed Forces and looking after the children our heroes have left behind is close to his heart."
Harry, a former army officer and veteran of two tours in Afghanistan, has been a prominent campaigner for military veterans.