Princess Michael of Kent is reported to have described public breastfeeding as a "dreadful practice".
According to the Daily Mail, when asked about breastfeeding in public, The Princess, who is married to the Queen's cousin Prince Michael of Kent, said: "My advice to women is don't breastfeed - it's a dreadful practice.
"I didn't breastfeed. My nanny said it was disgusting."
In a statement issued by her spokesman Simon Astaire, the Czech-born princess has now added: "It's not something I would do in public but everyone has a free choice."
The Princess, whose son Lord Freddie Windsor and daughter Lady Gabriella Windsor are grown up, is understood to have had difficulty breastfeeding her children.
Emily Slough, of the Free to Feed campaign group, said it was damaging for mothers to face negative comments about breastfeeding.
Ms Slough, from Rugeley, Staffordshire, who founded Free to Feed in March after she was labelled a ''tramp'' on Facebook for breastfeeding in public, said: "I just think somebody with that kind of social standing should think about what they're saying.
"It's incredibly damaging for women trying to breastfeed their children and trying to do the best for them to hear negative comments about breastfeeding.
"I don't understand what the logic is. It's not disgusting. It's not dreadful. That's how we're supposed to feed our children.
"If they can't get over the whole women and breasts things - it's just babies eating."
The Princess's comments follow recent debate about whether it is acceptable to breastfeed in public, with Ukip leader Nigel Farage being one of the political figures to wade in with their opinions.
He used his LBC phone-in show to suggest mothers could ''sit in the corner'' in restaurants to avoid offending people.
Mothers staged a mass ''nurse-in'' outside Claridge's hotel in London last week to protest over an incident in which a woman was asked to cover herself up when she was breastfeeding in the restaurant.
Prime Minister David Cameron came out in support of breastfeeding in public following Mr Farage's remarks, with a Number 10 spokeswoman saying: ''The Prime Minister shares the view of the NHS, which is that breastfeeding is completely natural, and it's totally unacceptable for any women to be made to feel uncomfortable when breastfeeding in public."
The Duchess of Cambridge is thought to have breastfed Prince George, but is unlikely to have done so in public for fear of media intrusion.
Diana, Princess of Wales, breastfed her sons, while the Queen is said to have breastfed Prince Charles until she contracted measles when he was two months old.
But Queen Victoria, a mother of nine, called breastfeeding "a horror" and employed wet nurses instead.