Threatening graffiti which read “this is the first warning” and a swastika symbol was found on the door of Red Cross’s Lyngbygaard asylum centre in the early morning hours of Thursday.
A minivan belonging to the centre was also set on fire, police said the car did not pose any danger to the centre’s residents and “This is the third time that the asylum centre has been subjected to vandalism with an apparent political motive.”
The other two incidents occurred on March 20 and July 31, according to TV2.
Police said on Thursday that they believe the same people were behind all three incidents of vandalism, but had not yet identified any potential subjects.
The graffiti also featured the letters DNSB, an abbreviation for Denmark's National Socialist Movement, just as in previous incidents.
A volunteer at the asylum centre, Erik Boye Kirk, said that the first two incidents were largely written off as pranks, "but it isnt that now that a car has been set on fire."
Kirk, who talked to broadcaster DR added that “cynical” people who vandalized Lyngbygaard were likely inspired by recent events in Germany.
The vandalism of the asylum centre in Lyngbygaard comes amid a rise of attacks on refugees across Europe.
The centre hosts 120 asylum seekers and according to local sources, this is the third attack on the facility in recent months.
In the previous incidents DNSB was also spray-painted on the building.
The first two attacks were written off as pranks but now police are investigating whether they were all politically motivated.
Germany is also one of the European countries which has had the most far-right protests and riot attacks on the shelters for asylum seekers.
On Tuesday in Leipzig, two drunk men broke into a refugee housing block carrying a knife and an unknown attacker set a fire in a building that was scheduled to be used as refugee accommodation in Leipzig.
That fire was the third within a week set at refugee and asylum-seekers homes in Germany. German Chancellor Angela Merkel condemned the incidents as “repulsive” and “shameful”.
According to the International Organisation for Migration, almost a quarter of a million refugees have crossed the Mediterranean to reach Europe this year.
About half that number have come to the Greek islands, with numbers surging in the summer due to calmer weather making the voyage relatively less risky.
The huge number of refugees arriving in Greece is putting the countries already strained economic resources under extreme pressure.