Henrik, 83, who married Queen Margrethe in 1967, was later named the Queen’s Prince Consort, but has repeatedly said he would have liked to be named King Consort.
“It is no secret that the prince for many years has been unhappy with his role and the title he has been awarded in the Danish monarchy.
“This discontent has grown more and more in recent years,” the Royal Danish House’s director of communications said.
“For the Prince, the decision not to be buried beside the Queen is the natural consequence of not having been treated equally to his spouse - by not having the title and role he has desired,” she added.
Prince Henrik retired last year and renounced his title of Prince Consort.
Since then, he has participated in very few official duties and instead spent much of his time at his private vineyard in France, although he is still married to the queen and they officially live together.
In Denmark, a princess traditionally becomes queen when her husband takes the throne.
It had been expected that the prince would be buried next to the Queen, 77, who, it is planned, will be interred in the Roskilde Cathedral in a sarcophagus made by Danish artist Bjorn Norgaard.
Born Henri Marie Jean André de Laborde de Monpezat in France in 1934, Henrik has two sons with the queen, Crown Prince Frederik and Prince Joachim.