Berlin and Nuremberg also saw protests turn violent.
About 10,000 leftist demonstrators waged running street battles in the Hamburg district of Barmbek with both neo-Nazis, who had staged marches earlier, and with the police. Eyewitnesses reported rioters pelting police with stones and firecrackers.
The police used water cannons to disperse protesters, but violence continued past midnight as about 200 people continued to build barricades and burn cars and trash cans.
Police arrested 59 people, of whom all but 11 were juveniles. Twenty-six of about 2,500 police involved and an unknown number of demonstrators were injured.
"The naked aggression and violence originated with the rightists," police spokesman Peter Born told German press agency DDP on Friday in Hamburg.
German press agency DPA cited eyewitnesses to report several leftists were injured after police struck them with batons when they tried to break through a police line.
After peaceful May 1 demonstrations and outdoor festivals, Berlin - traditionally hardest hit by May Day rioting - also saw widespread violence in the district of Kreuzberg. Rioters attacked police with cobblestones and bottles.
The city's police commissioner, Dieter Glietsch, narrowly avoided being assaulted by rioters, according to a police spokesman.
Still, police told DPA it was the most peaceful May Day in Berlin in 14 years.
One hundred and thirty-eight rioters were taken into custody in Berlin, and 90 police were injured - an improvement over the 115 police injured last year, officials said.
In the southern city of Nuremberg, lesser clashes also broke out alongside another rally by the neo-Nazi NPD party. Police there kept neo-Nazi and leftist groups apart with barriers.