The post racked up almost 40,000 likes in just seven hours, with many users praising the York family for their continued close bond.
"Love your family. So so much respect for your mum and dad and how strong you are together," one British fan wrote.
Princess Eugenie's sports day post comes days after her cousin-in-law Meghan Markle sparked outrage with her 'diva' behaviour at Wimbledon.
The Duchess of Sussex delighted royal fans when she made a surprise appearance at Court 1 with best friends Lindsay Roth and Genevieve Hillis to watch her close pal Serena Williams in action last week, but the happy occasion quickly turned sour when royal protection officers repeatedly asked spectators to stop taking photos around Meghan - despite their cameras being focused on tennis ace Serena, not the Duchess.
Meghan's bodyguards said she was attending Wimbledon in a "private capacity" and warned tennis fans against taking pictures of the Duchess to allow her to "engage with people rather than camera phones", royal sources told Daily Mail.
But many have questioned the validity of this tack after the match on Court 1 was watched by 12,000 in situ with millions tuning in on TV.
The controversy follows uproar over Meghan and Prince Harry's renovations to Frogmore Cottage, which cost the British taxpayer $4.3 million.
