In a statement released by the palace Ms Markle said she hoped “he can be given the space he needs to focus on his health”.
The announcement comes just two days before the nuptials are due to take place.
Ms Markle 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.”
Mr Markle, 73, is in Mexico, recovering after undergoing heart surgery on Wednesday to implant three stents.
The reclusive former TV lighting director, who had been due to walk his daughter down the aisle, was caught up in controversy after allegedly being caught staging photographs with the paparazzi.
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He reportedly pulled out of attending the ceremony in St George’s Chapel on 19 May to avoid embarrassing his daughter, but then later said before his surgery that he wanted to be part of history and hoped to be there, according celebrity website TMZ.
Before the news had been confirmed, Ms Markle’s brother appeared to criticise Kensington Palace for failing to provide sufficient guidance to their father in the run-up to the wedding.
“It would have been better for the palace to have guided him, as well as us for that matter, to ensure the focus is on Harry and Meg and not her family back in the States.
“They should have intervened and guided us when Meg and Harry’s relationship was first made public,” he told The Daily Mirror.
Pictures of Mr Markle appeared in a number of British newspapers which, it was later alleged, had been staged, amid wall-to-wall coverage of the wedding build-up.
Additional reporting by PA