Edward, the youngest son of Queen Elizabeth, and his wife Sophie announced the change of plans on the eve of a seven-day trip to the region to celebrate the Queen's Platinum Jubilee, marking her 70 years on the throne.
They will go ahead with plans to visit the island countries St Lucia, Saint Vincent and the Grenadines and Antigua and Barbuda starting on Friday, Buckingham Palace said.
The royal couple still plan to visit Grenada at a later date.
The change was made after consultations with the Grenadine government and the governor general, the Queen's representative on the island.
The decision comes as Caribbean countries debate their relationship with the British crown.
Prince William and the Duchess of Cambridge were sharply criticised last month for being "tone deaf" and perpetuating images of Britain's colonial rule during a tour of Belize, Jamaica and the Bahamas.
Though many people welcomed the royals, they were also greeted by protesters demanding an apology for Britain's role in the enslavement of millions of Africans and reparations for the damage caused by slavery.
During a speech in Jamaica, William expressed his "profound sorrow" for slavery but stopped short of offering an apology.
William also recognised the changing nature of the connections between the United Kingdom and its former colonies and said it was up to the people of these countries to decide whether to continue their links to the crown.
"We support with pride and respect your decisions about your future," William said during a speech in Nassau, the capital of the Bahamas.
"Relationships evolve. Friendship endures."
The Earl and Countess of Wessex were likely to face similar calls for a UK apology during a visit to Grenada, where activists had requested an audience with the royal couple.
The itinerary for the remainder of their trip is decidedly non-political.
In Antigua and Barbuda, Edward and Sophie will hear about the importance of sport in the community and attend a reception for local artisans and non-profit organisations.
While visiting Saint Vincent and the Grenadines, Edward will meet athletes training for the Commonwealth Games and Sophie will speak to women in leadership roles about the community's response to the eruption of the La Soufriere Volcano.
In Saint Lucia, the couple plan to visit the Pigeon Island National Landmark and the Sulphur Springs, a dormant volcano whose mud baths are a tourist attraction.
They will also attend a service to mark the Queen's 70-year reign.
The royals are visiting the three countries as representatives of the Queen who celebrates the 70th anniversary of her reign this year.
During those seven decades she has been the head of state for the UK and 14 "realms" that were once colonies of the British Empire and are now independent countries.
