Earlier this week Thomas Markle cited the operation as his reason for not attending the royal wedding on Saturday.
He says he is now out of surgery, but will be staying in hospital for a few more days.
"I'm OK. It will take a long time to heal," he told TMZ entertainment television news channel. "Staying in the hospital a few more days. Not allowed to get excited."
Thomas Markle appears to have successfully undergone heart surgery, the report said. Earlier he said doctors would "go in and clear blockage, repair damage and put a stent where it is needed".
He has reportedly changed his mind about attending the wedding ceremony more than once, and now seems set to miss it.
Before the operation Thomas Markle had told TMZ he wanted to walk his daughter down the aisle.
"I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle," he was quoted as saying.
Thomas Markle has been involved in controversy since it was revealed he allegedly staged a series of photos captured by an American paparazzo.
According to TMZ, Markle said staging the photos was "stupid" but not a serious transgression.
Meghan Markle's half-sister, Samantha Markle, recently said she was the "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 worked on popular TV shows "Married with Children" and "General Hospital," according to the Internet Movie Database.
He met Meghan's mother, Doria Ragland, at a Hollywood studio in the late '70s and the pair split when their daughter was young.
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