The extremists are known to police as football hooligans, and had wrought chaos Monday at an area of the eastern city known to be left-leaning, just as thousands of far-right supporters of the anti-migrant PEGIDA movement were gathering at a peaceful demonstration, authorities said.
News website Spiegel Online also published a picture of a kebab shop with a smashed window.
Germany has been outraged by a rash of crime targeting women at New Year’s festivities in Cologne in the west that has been blamed on migrants.
As thousands rallied to blame refugees for the violence, a group of hooligans broke away and smashed windows, burned cars and rubbish bins and shot off pyrotechnics that set a floor of a building on fire.
In return, left-wing radicals vandalised a bus that had been chartered by the hooligans, police said.
In all, 57 offences were committed that night, police said.
Germany has recorded a sharp jump in crime attributed to the far-right in tandem with the surge in asylum seeker arrivals which reached 1.1 million last year.
Police said groups linked to Cologne’s extremist hooligan scene had used social media to organise gatherings in the inner city Sunday evening, and launched a spate of attacks against Pakistani, Syrian and African men.