The asylum seekers from Syria, Somalia and Egypt were waiting at a tram stop in Frankfurt an der Oder, a Brandenburg town an hour east of Berlin, when a group of men approached them.
The men started insulting the asylum seekers, police report, and then one man punched the youngest of them, a 17-year-old refugee from Syria, directly in the face.
The asylum seekers fled, with two of them making for a nearby shopping centre. But they were chased down by three men who caught them and started beating them.
As the men continued to insult and abuse them, other members of the public joined in, hurling racist abuse at them.
The victims didn't suffer any visible injuries and there was no need to call an ambulance, a police spokesperson said.
Police were able to arrest one man with the help of witnesses. They measured 3.7 parts per thousand of alcohol in his blood - or seven times over the legal limit for driving a car.
Investigators have now opened an investigation for dangerous bodily harm and displaying banned political symbols.
A report published by the federal interior ministry on Monday showed that 2015 was a record year for extremist political crime by far-right and far-left movements.
Interior Minister Thomas de Maizière described the figures as “practically exploding” and warned of a brutalization taking place in German society.
Right-wing criminality shot up by 35 percent in 2015 to 23,000 recorded instances, or about 60 percent of the total number of political crimes.