The humble act has been applauded by many Fijians and people from around the world, with many commenting about its uniqueness on social media.
One woman said: "If you see in our custom, we kneel and clap in the presence of royalty - and she clapped as well! Big love to Princess Anne. Fiji is the first to kneel while being adorned with medals. Respect, humility, honour, roots.''
On New Zealand screens, veteran commentator Keith Quinn was heard referring to one of the players kneeling - before seemingly realising it is a special act.
"So tall he's got down on his knees to receive his medal from Princess Anne. And it looks like that's the way the big tall men of Fiji are going to receive their medals.
"Again, this is a famous first - never seen players go to their knees to receive their medals before,'' Quinn says.
In 2013, Fijian soldier Sergeant Rusiate Bolavucu also showed off the cultural custom when he sat on the ground after speaking with Her Majesty the Queen Elizabeth during a royal tour in Kendal, Cumbria.
The act shocked members of the public who had gathered around the area.
However, the Queen, who has visited the Pacific numerous times, smiled at him in understanding.