Thomas Markle told TMZ he was due to have surgery to repair coronary damage and clear a blocked artery, after reportedly suffering a heart attack a week ago.
Doctors "will go in and clear blockage, repair damage and put a stent where it is needed", Markle, an Emmy-winning Hollywood lighting director, was quoted as saying.
He had hoped to walk his daughter down the aisle during the meticulously-planned ceremony at Windsor Castle's St. George's Chapel on Saturday, "but now he realises it's all but impossible given the upcoming surgery," TMZ said.
There had been confusion over Thomas Markle's plans after he apparently changed his mind repeatedly in recent days.
After originally planning to attend, he then decided not to travel from his home in Mexico to spare his daughter embarrassment after a paparazzi scandal where he posed for staged pictures.
On Tuesday TMZ initially reported an about-face from Markle, who said he would try to attend after he had been contacted by his daughter via text -- before he revealed once more that his health was preventing him from travelling.
"I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle," the 73-year-old told TMZ from hospital.
- 'Deeply personal moment' -
Thomas Markle said his ex-wife Doria Ragland, 61, would be a good choice to walk their daughter down the aisle in his place, according to the website.
Ragland, who has reportedly already arrived in Britain, is expected to spend Friday night with Meghan in a plush hotel before travelling with her by car to Windsor Castle.
US actress Markle, 36, grew up in Los Angeles and remains close with her parents, who divorced three decades ago.
Harry's Kensington Palace office issued a brief statement that did not mention Markle's heart drama, but said: "This is a deeply personal moment for Ms Markle in the days before her wedding.
"She and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this difficult situation."
The palace could not be reached for further comment.
- 'Positive photos' -
Thomas Markle told TMZ he had agreed to pose for a paparazzi photo shoot in a bid to rehabilitate his image, rather than for money, but that he now regretted the move.
The pictures -- in which he was being measured for a suit and admiring a photo of the future royal couple on his computer -- sold for $100,000 (83,000 euros), according to British tabloid the Daily Mirror.
TMZ said he had suffered a heart attack last week due to stress and that he was continuing to suffer from chest pains.
Meanwhile, Meghan Markle's half-sister Samantha Grant, who has criticised the bride-to-be's relationship with her father's side of the family, revealed her dad was feeling "quite depressed" and had indeed suffered a heart attack.
"I don't know as of today what his plans are, but there's a very real concern," she told Britain's ITV television.
Whether he attends the wedding will be based on "whether or not it's safe" for him to go, said Grant.
She said her father had "suffered at the hands of the media" who had presented him "in the most horrible ways".
Staging the photos was intended to counter the way he had been "so unfairly presented in the media as being sort of shabby".
- 'Circus' in town -
Kensington Palace's attempts to project a sense of serenity around the wedding preparations have been clouded by Markle's relatives, who have not been invited to Saturday's nuptials following stories of bust-ups, heavy drinking and an arrest.
Meghan's half-brother Thomas Markle Junior accused her of shunning the family in an open letter last month.
In what The Daily Telegraph newspaper called "the circus" surrounding the wedding, Tom Junior's ex-wife Tracy Dooley -- also not invited to the wedding -- rolled into London with her two sons Tyler and Thomas.
"We're here! Yay!" she said, posting pictures of London landmarks, after they were spotted pushing luggage through Heathrow Airport.
The Dooleys are reportedly appearing on ITV's Good Morning Britain programme as part of their royal wedding coverage.
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