The announcement came a week after the United States said it planned to release five Britons and the Dane.
The man has not been named by authorities, but Danish media have identified him as 30-year-old Slimane Hadj Abderrahmane. He was transferred to Guantanamo Bay in February 2002 after being captured in Afghanistan or Pakistan (search).
"The police have, according to an agreement with him and the family, made housing available for the next few days," the Foreign Ministry said in a brief statement.
It said the man did not wish to speak to reporters.
The government has earlier said he won't face charges in Denmark, but would be monitored by intelligence agents.
Danish media reports said Abderrahmane, whose mother is Danish and father is Algerian, briefly studied mathematics at the University of Aarhus, in western Denmark. He eventually left Denmark via Algeria and disappeared until his arrest.
More than 600 prisoners accused of links to Al Qaeda or the former Taliban regime in Afghanistan are being held at Guantanamo Bay.