The group started a conversation with the 93-year-old when they saw her walking with her protection officer Richard Griffin at her holiday home in Aberdeenshire, Scotland. The tourists did not realise who they were speaking to when they asked whether she lived nearly. When she replied that she did, they then asked if she had ever met the British head of state.
Not wanting to give herself away, the Queen pointed towards Mr Griffin and said “No, but this policeman has.”
The group then left a short while later without clocking who they had just spoken to.
The Queen was even wearing her well-known casual attire of a headscarf and tweeds.
Mr Griffin, who has worked with the Royal Family for more than 30 years, shared this story with The Times.
The Queen leads a more low-key lifestyle when she stays at Balmoral.
The castle has been a residency of the British royal family since 1852.
The grounds cover an area of around 50,000 acres.
The estate also includes forestry and farmland, along with herds of deer, Highland cattle and ponies.
Every summer the Queen and other members of the Royal Family head up to Scotland.
Some of the royals who always pay the Queen a visit include The Duke and Duchess of Cambridge and their children George, Charlotte and Louis, as well as Prince Charles and Camilla.
Meghan Markle, Prince Harry and the York family also spend time there.
Princess Eugenie said her grandmother was “most happy there”.
She said on ITV’s documentary Our Queen at 90: “It’s the most beautiful place on earth. I think Granny is the most happy there.
“I think she really, really loves the Highlands…walks, picnics, dogs, a lot of dogs, there’s always dogs, and people coming in and out all the time.
“Family-wise we’re all there, so it’s a lovely base for Granny and Grandpa to be.
“And for us to come and see them up there where you just have room to breathe and run.”