Seemingly written by one of the Cambridge's staff, the letter read, "The Duke and Duchess of Cambridge have asked me to thank you for your letter, in which you invite Prince George to your 6th Birthday party.
"I am sorry that it took so long to reply.
"Their Royal Highnesses were extremely grateful for your kind invitation. Having given careful consideration to the possibilities, however, I very much regret that Their Royal Highnesses reluctantly feel they have to decline.
"The Duke and Duchess of Cambridge were immensely touched that you should take the trouble to write as you did to their son, Prince George.
"It really was most thoughtful of you and Their Royal Highnesses have asked me to send you their warmest thanks and best wishes.
"Nevertheless, I hope you enjoy your birthday."
It comes after the prince celebrated his own birthday last month.
To mark the occasion, a new portrait was released of George wearing a light blue polo shirt, flashing a big grin and looking just like his father.
Taken by the Duchess, the royals posted the photo to their social media accounts and captioned the post, "George is turning 9!"
Later they added in a statement: "The Duke and Duchess of Cambridge are delighted to share a new photograph of Prince George ahead of his ninth birthday tomorrow".