The Royal Household announced on Tuesday that neither leader would be attending the Windsor Palace nuptials, with political figures kept off the guest list entirely.
It means that Barack Obama, with whom Harry has a close relationship, will also be missing from the day’s proceedings.
A spokesperson for the palace said: “It has been decided that an official list of political leaders – both UK and international – is not required for Prince Harry and Ms Markle’s wedding.
“Her Majesty’s Government was consulted on this decision, which was taken by The Royal Household.”
There had been much speculation over whether 71-year-old Trump would be invited to watch the couple tie the knot on May 19.
While world leaders have been invited to royal weddings in the past, Meghan - a staunch Hillary Clinton supporter – has previously dismissed the president’s rhetoric, calling it “divisive” and “misogynistic”.
The move is yet another signal that Harry and Meghan’s wedding will be much more personal than the Duke and Duchess of Cambridge’s 2011 ceremony, which was a semi-state occasion.
Around 2,000 people packed into Westminster Abbey to watch the young couple exchange vows, with PM David Cameron, his deputy Nick Clegg and Labour leader Ed Miliband among the crowd. May was also in attendance as the UK’s then-Home Secretary.
However, Harry and his bride-to-be have invited 2,640 members of the public inside the grounds of Windsor Castle on their wedding day to watch the pair and their guests arrive and leave.
The guest list, which was decided by the UK’s Lord Lieutenants and announced by Kensington Palace today, includes 30-year-old Philip Gillespie from Northern Ireland, who lost his leg in an IED incident in Afghanistan before raising funds for ABF The Soldiers’ Charity.
Deaf schoolboy Reuben Litherland, who started sign language lessons at his school, and 12-year-old Manchester Arena attack survivor Amelia Thompson have also been invited.
The trio, along with almost 1,200 other people who have made “notable contributions to the local community”, will be joined by 200 guests from charities the royal couple work with, as well as 100 local school pupils and 500 members of the royal household.