Stalking deer is a historic practice in the Scottish Highlands and is essential to control the population of deer, which have no natural predators in the UK.
According to Express, a spokesman for the League Against Cruel Sports said, "Killing deer for a sport is a horrible pastime. It's very sad that she has chosen to participate in this cruel sport.
"It's hardly setting a good role model for young women, killing animals and I can't see that this will do her reputation any good whatsoever.”
PETA also compared Kate to Princess Diana, pointing out that William's mother took a stance against hunting.
"Some have compared Kate to Diana, but Diana never wore fur and she also turned against blood sports."
The late-Princess of Wales was criticised after wounding a stag while hunting with the Prince of Wales prior to their royal wedding.
Despite the fact Diana was "blooded" by ghillies – a ceremony which involves a hunter's forehead being smeared with the blood of their first kill – she vowed never to take part again.
WATCH: Kate Middleton and Meghan Markle at Wimbledon a 'PR exercise' says New Idea Expert
William and Kate will be visiting the Queen's estate in Balmoral with their children Prince George, Princess Charlotte and Prince Louis over Britain's summer.
However, with reports of tension between the Duke and Duchess of Cambridge and Prince Harry and Meghan Markle, the family may delay their trip to Balmoral until the Sussex royals have left Scotland.
Royal expert Robert Jobson told the Daily Mail that William and Kate are waiting until Meghan and Harry return to Windsor before heading up to Balmoral.
For more royals news, pick up a copy of this months New Idea Royals magazine.