Queen Margrethe and the couple's two sons, Prince Frederick and Prince Joachim, were with Prince Henrik when he died at the royal residence Fredensborg Palace, on the Danish island of Zealand, a palace statement said.
Prince Henrik died late on Tuesday aged 83 and flags are flying at half mast across Denmark.
He was titled prince consort - the husband of a reigning queen but not a king - and he wasn't in the line of succession, his oldest son Crown Prince Frederik being the heir.
Denmark's Prince Henrik, the father-in-law to Australian-born Crown Princess Mary, has died aged 83.
Prince Henrik of Denmark attends a Gala Dinner for Iceland's President at Amalienbog Castle in Copenhagen, Denmark, Jan. 24, 2017. After he was rushed back to Copenhagen, doctors revealed he had a tumor in his left lung.
Henrik lived his first five years in French Indochina.
Henri Marie Jean André de Laborde de Monpezat was born on 11 June 1934 in Talence, Gironde, France, to Count André de Laborde de Monpezat and Countess Renée de Monpezat, née Doursennot.More news: How to Watch Olympic Men's Hockey Online
In a period of mourning, the Royal Family will not participate in "social or entertaining events" until March 14, the family said in a statement.
The Danish royal family has no political authority, but is one of the world's oldest kingdoms and prides itself on stability. He studied law and politics at the Sorbonne in Paris and Chinese and Vietnamese languages.
He served in the French Army during the Algerian War and worked in the French Foreign Affairs ministry.
Upon marrying her, he changed his name to Henrik, converted from Catholicism to Protestantism and renounced his French citizenship to become a Dane.
With Queen Margrethe in Cahors, France in 2003.
The prince moved to Denmark in 1967 ahead of his June wedding to the then-crown princess, but he found it hard being relegated to a supporting role.
"His Royal Highness The Crown Prince has thus discontinued his stay in South Korea, where he was in conjunction with the winter Olympics". He later vented his frustrations at never having been made king and being outranked by his wife. In latest years, he said on numerous occasions that he was frustrated with his life in Denmark and the title of prince consort, which he waived after his official retirement in late 2015. A spokesperson stated that the Queen accepted his decision.