Mr Markle told celebrity news website TMZ, at his home in Mexico, that he had decided not to attend his daughter's wedding to Prince Harry.
Kensington Palace issued a statement saying it was "a deeply personal moment for Ms Markle".
It follows Mail on Sunday reports that Ms Markle's father had staged pictures for a paparazzi photographer.
The widely circulated photographs showed him being measured for a wedding suit and looking at newspaper stories about his daughter.
He is reported to have said that he didn't want to cause his daughter embarrassment by attending the wedding.
A Kensington Palace spokesman 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."
Mr Markle had been due to meet Prince Harry for the first time this week, as well as the Queen and the Duke of Edinburgh, before walking his daughter down the aisle at St George's Chapel in Windsor Castle.
Meghan 'hopeful' father can attend
The BBC's royal correspondent Nicholas Witchell said he understands Ms Markle is distressed and concerned for the wellbeing of her father, who has been described as a rather shy and reclusive figure.
He added: "I understand it is still very much Meghan Markle's wish that her father should be there on Saturday to support her."
The controversy surrounds pictures of Mr Markle, which were published earlier this month in a number of newspapers showing him in a series of wedding related activities - apparently unaware he was being photographed.
Samantha Markle, Ms Markle's half-sister, has claimed she is to blame for the photographs.
She tweeted: "The media was unfairly making him look bad so I suggested he do positive photos for his benefit and the benefit of the royal family.
"We had no idea he would be taken advantage of. It was not for money."
The wedding will take place on 19 May at 12:00 BST at St George's Chapel in Windsor.
With five days to go, Kensington Palace had earlier revealed that Miss Markle will spend her last night before getting married at a luxury Berkshire hotel with her mother, Doria Ragland.
Prince Harry will be staying 15 miles away at the Dorchester Collection's Coworth Park in Ascot, with his brother, the Duke of Cambridge.