Followers of the royal family were quick to voice support for the social media post, which racked up more than 15,000 likes and hundreds of comments in a matter of hours.
One fan wrote: "I feel like you are the coolest young royal - humble and real. I dig it! Keep it up, Mrs. Jack Brooksbank."
Last month, the granddaughter of Queen Elizabeth II was announced as the new patron of Horatio's Garden, a charity that creates accessible gardens at spinal injury centres across Britain, Hello! Magazine reports.
Princess Eugenie famously underwent surgery for scoliosis when she was just 12-years-old.
The younger sister of Princess Beatrice made a beautiful statement on her royal wedding day to Jack Brooksbank at St George's Chapel in Windsor Castle last October by choosing a custom Peter Pilotto wedding dress which showed off the long surgical scar running down her back.
On her special day, Princess Eugenie also paid a subtle tribute to her mum the Duchess of York and cousin in-law Kate Middleton, Duchess of Cambridge, who wed future King of England Prince William eight years ago at London's Westminster Abbey.
The Princess of York drew inspiration from Kate by choosing the same wedding car - Queen Elizabeth's 1977 Rolls Royce Phantom VI - used by the mother-of-three in 2011, Express.co.uk reports.
Famously family oriented Eugenie chose the Duke and Duchess of Cambridge's only daughter Princess Charlotte as one of her bridesmaids, as well as Savannah and Isla Phillips - daughters of Princess Anne's son Peter - and Mia Tindall, Zara Tindall's daughter.
Eugenie's wedding dress honoured flame-haired mum Fergie with delicate shamrock embroidery as a nod to the Duchess' Irish heritage.
WATCH this video to relive the magic of 2018's royal weddings!
Since the start of the year, Eugenie has been the subject of intensifying media attention amid rumours she is expecting her first child.
If the reports are accurate, the British public could look forward to the arrival of another royal baby before 2020 - a playmate for the Duke and Duchess of Sussex' newborn son, Archie Harrison!
Buckingham Palace has yet to comment on the reports.