Samantha Markle -- who has reportedly not spoken to her sister for several years -- did not specify the timing of her father's heart attack, but told the Good Morning Britain program that her father was "quite depressed over the unbelievable series of events involving the media."
She reiterated in the interview that she was very concerned for his health, but said she did not want their father to miss out on the big day.
"I wanted to see him go. I didn't want him deprive of that. But clearly the propriety should be whether or not it is safe for him to do that," Markle added.
Samantha Markle previously revealed she was "culprit" who urged their father to stage the photos in an ill-fated bid to improve his image. She said her father had "suffered at the hands of the media" and had decided "enough is enough."
Thomas Markle is a former lighting director who had worked on popular TV shows "Married with Children" and "General Hospital," according to IMDB. He met Meghan's mother, Doria Ragland, at a Hollywood studio in the late 70s but the pair split when their daughter was still young.
CNN understands that both Prince Harry and Meghan Markle are very concerned about the pressure Thomas Markle is under and are keen for the media to give him space.
Meghan Markle is understood to be upset about the photos being staged, but is very close to her father and still wants him to walk her down the aisle on Saturday.
Royal biographer Penny Junor said that following the furore, Harry will likely feel "horribly responsible" for the problems besetting his soon-to-be father-in-law.
"(Harry will be feeling) guilty and frustrated and impotent; he's tried to protect her as much as he could and here he is at the last fence, failing miserably, but it's not his fault," Junor told CNN.
She added the situation will also be "incredibly difficult" for Meghan.
"She's got those wretched half-siblings who are making trouble for her as well, and uncles who seem to be complaining they haven't been invited despite not having seen her for years," Junor added. "We all have these kinds of relatives tucked away somewhere in our families but those dramas are not dished up for public consumption."
Thomas Markle apparently confirmed on Monday he would no longer be walking his daughter down the aisle after he allegedly staged a series of photos captured by an American paparazzi photographer.
Markle reportedly told American publication TMZ he was going to skip the highly-anticipated wedding so as not to cause embarrassment to the royal family or his daughter.
CNN has reached out to Thomas Markle for comment by phone and over email but has not yet received a response.
In an unusual move, Kensington Palace issued a statement on Monday night, describing the situation as a "deeply personal moment for Ms Markle in the days before the wedding."
A Kensington Palace spokesman added that "She and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this difficult situation."
Thomas Markle had been due to fly into the UK in the days before the wedding to spend time with the British royal family, including Queen Elizabeth II and the Duke of Edinburgh. Harry has yet to meet his fiance's father.
With the big day quickly approaching, the final touches for the wedding were being locked down, including the food menu for the reception.
Mark Flanagan, the head chef in the Royal Kitchen at Windsor Castle revealed the couple have taken an active role in the selection of produce offered to their 600 guests. He said Harry and Meghan had been to several sampling sessions back in March.
It has also been revealed that the couple will spend their final night before the wedding at separate luxury hotels near Windsor.
Harry will be joined by his brother and best man, Prince William at the lavish Coworth Park Hotel, while Meghan and her mother will stay at the Cliveden House Hotel.