"His Royal Highness Prince Henrik died on Tuesday, February 13, at 23.18 quietly at Fredensborg Palace", the statement said.
Prince Consort Henrik died in his sleep with Margrethe and the couple's two sons at his side, according to the statement.
The French-born prince, who was the father-in-law of Australian-born Crown Princess Mary, was diagnosed with a benign tumour two weeks ago.
In his early 30s, Prince Henrik worked in the Asia section of the French Ministry of Affairs at the French embassy in London.
Being greeted by his family (L-R) Queen Margrethe, Crown Prince Frederik and Crown Princess Mary.
"I didn't marry the queen to get buried at Roskilde", he said in August 2017.
Prince Henrik did not take it lightly when, in 2002, Crown Prince Frederik was chosen to represent Queen Margrethe at a New Year's ceremony, instead of him.
Henrik is survived by his wife, two sons and multiple grandchildren.
Xiaomi Mi TV 4 FAQ, pros, cons, user queries and answers
Both the front and rear cameras on the Redmi Note 5 Pro offers the portrait mode for capturing photos with blurred background. The Redmi Note 5 will be packed with 3 GB RAM for the 32 GB variant and will have 4GB RAM in its 64GB storage model.
Henrik had his fair share of engagements and patronages, as well as accompanying the queen on state visits and other functions. He published several poetry collections, some illustrated by the queen, as well as books on cookery and his memoirs.
After a 2009 Danish referendum supported the equality of the sexes in the royal succession, Henrik remarked: "I hope that men will be as equal as girls", spurring further debate and briefly finding support in parliament in favour of allowing Prince Henrik the title of king.
As of 2005 he was addressed as prince consort. She was crowned queen five years later.
Prince Henrik has been at the centre of controversy after he announced he did not wish to be buried next to his wife, Queen Margrethe, saying he was unhappy she never acknowledged him as her equal.
The following month, the palace announced that the prince was suffering from dementia and that the impact was assessed to be "greater than expected" for his age.
He formerly held the title of Prince Consort but renounced that title when he retired from his official duties in 2016.
"For the Prince, the decision not to be buried beside the Queen is the natural outcome of not having been treated equally to his spouse - by not having the title and role he has desired", the spokesperson told the wire service.