Police said that three mopeds were burnt shortly after midnight at the Nørrebro square Blågårdsplads, followed by a car fire in inner Nørrebro.
The mopeds were torched in the middle of a football field while the car, an Audi S6, was set on fire on Baldersgade.
Investigators said they had little information to go on.
“We don’t have any witnesses who saw anything and by the time police arrived there was nothing to find but we have some technical clues, primarily on the Audi,” police spokesman Henrik Stormer told broadcaster DR.
The incidents follow the burning of 21 cars over the weekend. The weekend fires were primarily in the Christianshavn and Amager districts, but one vehicle was also torched in Valby.
Prior to the new fires early on Tuesday, police said in a press release that they have “several good clues” about the weekend fires.
Copenhagen Police have been cautious about drawing parallels to Sweden, where at least 70 cars have been burnt in Malmö since July and car fires have occurred in cities including Stockholm, Gothenburg and Norrköping.
In Norway, the Oslo Fire Department reported that two cars had been set on fire there early on Tuesday but there was no word on whether a connection to the Swedish and Danish fires was suspected.