The prince will be cremated following the service.
In accordance with his wishes, half of his ashes will be spread at sea in Danish waters, and half in the gardens of Fredensborg Palace.
The funeral will take place at Copenhagen's Christiansborg Slotskirke, the palace also confirmed at a press briefing on Wednesday.
The prince will be taken from Fredensborg to Amalienborg Palace, the official royal residence, at 10am on Thursday.
A hearse carrying the prince will drive around Fredensborg on Thursday before continuing to Copenhagen, about 40 kilometres to the south.
A salute will be fired in honour of Prince Henrik on Thursday at 8am from Christian the Sixth's Battery at Kronborg Castle in Helsingør.
He will be taken to the Christiansborg Slotskirke church on Friday, in accordance with his own wishes.
The public will be able pay its respects to the prince at the church on Saturday, Sunday and Monday, where his closed coffin will be on display. The royal family will visit the coffin on Saturday morning, before the church is opened to the public.
Tuesday's ceremony will be not be a state funeral, also in accordance with Prince Henrik's wishes.
"It will be a funeral not containing the elements of a state funeral," palace head of communication Lene Balleby said.
Wednesday afternoon's announcement clears up any doubt about how Prince Henrik will be buried, given that he said in August last year that he did not want to be buried next to his wife, thereby breaking with the tradition of burying royal spouses together in Roskilde Cathedral.
The palace has not released any information as to who will attend the funeral other than the prince's immediate family.
The cause of his death is also yet to be confirmed.
"I cannot go into detail about what caused the prince's death. We have announced that he has been unwell on an ongoing basis. We have also said that various complications occurred. That aside, I can only say that he was an elderly man," Balleby said.
The prince's condition was reported to have seriously worsened on Friday. He had been in hospital in Copenhagen since late January for a pulmonary infection and a benign tumour in his left lung.