The prince is currently admitted to Copenhagen's Rigshospitalet.
"The tumour has fortunately been found to be benign.
"Prince Henrik will today be moved to the Department for Infectious Diseases to be treated for a lung infection. After treatment has been completed, His Royal Highness will stay at Fredensborg Castle," the statement read.
"As such, Her Majesty the Queen will today take up residence at Fredensborg Castle," the message continued.
On Sunday, the royal court announced that 83-year-old Prince Henrik, who is suffering from dementia, had been taken to hospital in Copenhagen after returning from a trip to Egypt.
"The Prince has since early January been in Egypt, where he was taken to hospital a few days ago… His Royal Highness has now returned to undergo further examinations," the palace said in a statement on Sunday.
Since then, the prince's two sons, Crown Prince Henrik and Prince Joachim, have sought to make public reassurances about his condition.
In September last year, the royal court announced that the Prince was suffering from dementia. Without revealing the full diagnosis, the palace said his illness "involves a deterioration of cognitive abilities".
The prince consort moved to Denmark in 1967 ahead of his wedding to the then-crown princess, but struggled to accept his supporting role.
He made no secret about his disappointment at not obtaining the title of king when his wife became queen in 1972 and has often spoken out about his frustrations.
Last year he revealed that he did not want to be buried next to his wife because he was never made her equal.
In her 2015 New Year speech, Queen Margrethe announced that her husband was to retire from public appearances.
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