He had been due to walk the 36-year-old divorcee down the aisle at the ceremony at the 15th Century St George’s Chapel at Windsor Castle on Saturday.
But a statement from the bride-to-be and former star of TV drama Suits, said: “Sadly my father will not be attending our wedding. I have always cared for my father and hope he can be given the space he needs to focus on his health.
“I would like to thank everyone who has offered generous messages of support. Please know how much Harry and I look forward to sharing our special day with you on Saturday.”
The news comes following media reports Mr Markle, 73, underwent heart surgery on Wednesday, following a heart attack last week.
Pictures of the award-winning lighting director had appeared in a number of British newspapers which it later emerged were staged, prompting him to drop out of the wedding, telling celebrity news website TMZ that he did not want to “embarrass the royal family or his daughter.”
But on Wednesday afternoon ahead of his daughter’s announcement, TMZ claimed Mr Markle would travel to the UK for the wedding if doctors allowed him out of hospital.
He was quoted as saying: “I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle. Of course I’d walk her down the aisle. This is a historic moment. I’d like to be part of history.”
Markle’s mother Doria Ragland, a yoga instructor and social worker, has arrived in Britain and is due to meet the 92-year-old Queen and her husband Prince Philip, 96, on Thursday. Royal commentators have speculated she will now walk her daughter down the aisle instead.
More than 5,000 media and support staff have registered for official positions in Windsor for the wedding, along with more than 160 photographers and 79 international TV networks, Kensington Palace said.
After the hour-long ceremony which will be attended by the Queen and senior royals, the couple will take part in a procession through the town’s ancient streets on a 19th Century Ascot Landau carriage pulled by four Windsor Grey horses.
Police are expecting more than 100,000 people to throng the streets outside the Castle, the Queen’s home west of London and the oldest and largest inhabited fortress in the world, and have said there would be tight security for the event.