The French-born prince has been unhappy with his title since being named prince consort -- rather than king consort -- upon the couple's marriage in 1967.
"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."
Balleby added that the decision had been accepted by the queen.
CNN contacted the Danish Royal House for comment on where Prince Henrik will be buried, but did not receive an immediate reply.
Queen Margrethe, 77, is still expected to be buried at the Roskilde Cathedral in a sarcophagus created by Danish artist Bjørn Nørgaard.
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.
The prince, who retired from public life last year, was born Henri Marie Jean André de Laborde de Monpezat in a suburb of Bordeaux, France, in 1934.
In his early 30s, Prince Henrik worked in the Asia section of the French Ministry of Affairs at the French embassy in London. It was during this time, in 1965, that he first met then-Princess Margrethe at a dinner party of mutual friends.
They were engaged in 1966 and married the following year.
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.
A previous version of this article misspelled Lene Balleby's family name and left out a word in her second quote. Both errors have been corrected.
CNN's James Masters and Hilary McGann contributed to this report