"Following a longer course of investigation, and most recently, a series of examinations conducted during late summer, a team of specialists at Rigshospitalet has now concluded that His Royal Highness Prince Henrik suffers from dementia," it said in a statement.
"The extent of the cognitive failure is, according to Rigshospitalet, greater than expected considering the age of the prince."
Prince Henrik is 83.
The French-born royal made headlines last month when he announced his refusal to be buried next to the queen when the time comes.
Long vocal about his frustration over being relegated to a supporting role, Prince Henrik explained in a newspaper interview on August 3rd that he was not on equal footing with his wife in life and therefore did not want to be so in death.
The palace said that his decision, which breaks with the royal tradition of being buried together in the Roskilde Cathedral, had been accepted by the queen.
Palace spokeswoman Lene Balleby told Danish TV2 on Wednesday that the prince's health condition had no bearing on his burial wishes, which he maintained.
In Wednesday's statement, the palace said the prince's cognitive failure "can be accompanied by changes in behaviour, reaction patterns, judgement and emotional life and may therefore also affect the interaction with the outside world."
As a consequence, the prince, who retired from public service in January 2016, will "further downgrade his future activities, just as patronages and honorary memberships will be considered."
Disappointed that his royal title of prince consort was never changed to king when his wife became queen in 1972, Henrik has often spoken out about his discontent, which did little to endear him to his subjects.
Born Henri Marie Jean Andre Count de Laborde de Monpezat on June 11th, 1934 in Talence, near Bordeaux, he met Margrethe, then the crown-princess, while he was stationed in London as a diplomat.
Upon marrying her, he changed his name to Henrik, converted from Catholicism to Protestantism and renounced his French citizenship to become a Dane.
By the time Margrethe acceded to the throne, the couple had two young children: Prince Frederik, born in 1968, and Joakim, born in 1969.