A 56-year-old male officer with the North Zealand Police was in stable condition on Tuesday after being stabbed at around 3.30am at the Sandholm asylum centre.
The officer was critically wounded in the attack, but police said shortly before noon that his condition had been upgraded to stable.
After an intensive search and investigation, police said that a 25-year-old stateless Palestinian was arrested as the sole suspected perpetrator. The man was scheduled to be sent out of Denmark after his asylum request was denied.
"The person is supposed to leave the country and that's why he's sitting in the departure centre," police spokesman Magnus Andresen said at a press conference.
"The case is being investigated as an attempted homicide," North Zealand Police said in a statement.
A large area was cordoned off around the former military barracks at Center Sandholm, Denmark's largest institution for asylum seekers, which currently houses around 600 people.
The facility, which lies around 20 kilometres (12 miles) northwest of Copenhagen, receives newly-arrived asylum seekers as well as those who have had their applications rejected and are due to leave the country.
Center Sandholm. Photo: Mariam Nielsen/Røde Kors
Andresen said that the injured officer noticed that there was a light on in an office that is normally locked at night. When he went in to check on it, he was attacked by the suspect, who stabbed the officer in the neck and shoulder. Police are investigating whether it was a break-in gone awry or if there were other motives behind the attack.
Andresen said that police do not believe that anyone else was involved.
Since Europe's refugee crisis began spilling into Denmark on September 6, at least 17,700 migrants have entered the country, according to police figures, but most have continued to neighbouring Sweden, which has more generous asylum rules.
Over the past three weeks, around 100 people per day have been applying for asylum, the Danish Immigration Service (Udlændingestyrelsen) said.