The whale is suspected to be ill. The Forest and Nature Agency says in a statement it has decided to let the whale "die a natural death" after consulting with experts in Denmark and abroad.
Spokesman Peter Bjerremand said he sailed out early Friday to gauge the 30-ton baleen whale's situation. He says it was still alive and its condition unchanged.
The 50-foot (15-meter) mammal was stranded Wednesday in the Vejle Fjord, 135 miles (220 kilometers) west of Copenhagen. It is believed to be about three to four years old.