"Hooray!" read the message. "Our friends in the English royal family, William and Kate have had a little boy called George Alexander Louis VII."
"Give them a huge 'like' to wish your congratulations :)" added the caption.
Given that more than 1,000 people then 'liked' the photo and several left their own touching messages, the Danish royal fans showed they are as happy about baby George's arrival as they are about their own royal family.
Since welcoming their son into the world on Monday 22 July the first-time parents, William and Kate, have been inundated with well wishes and gifts from all around the world.
Perhaps the most unique is from a pub in Cambridge that William and Kate visited last year in the early stages of the Duchess' pregnancy. The Greene King Pub the Fort St George of the small town have permanently reserved a seat for the Duke and Duchess of Cambridge's firstborn and marked it with a plaque.
"We want the family to know they are very welcome to come back any time, and there will always be a reserved space for the royal baby," said pub manager John Cecchini. "As he gets older, we will make sure the seat under the plaque grows with him."
The Danish royals have been celebrating their own close-knit family of late, appearing together for a photocall at Gråsten Palace.