The woman and her two children – aged around five and 15 – were travelling on the city's ring line at around 9:45pm on Saturday when two men embarked at Landsberger Allee, reports the Berliner Zeitung.
The men, aged 32 and 37, quickly began hurling racist insults at the family, who appeared to be of southeast European origin.
According to multiple witnesses, the men roared "Heil Hitler" and other Nazi slogans at the family, raising their right arms in Nazi salutes.
Referring to the woman and children as a "pack of asylum seekers," the men reportedly told them "we're the master race," adding "you're not Aryan."
32-year-old Christoph Sch. then exposed himself to the children before urinating on them.
Horrified witnesses called the police, and officers arrested the two men at the Frankfurter Allee station. The woman and children remained on the train.
Upon being breathalyzed, the men were found to have blood alcohol levels 2.3 and 1.8, roughly equivalent to eight and six bottles of beer, respectively.
Police have initiated proceedings against the pair for racist abuse and bodily harm.
On Monday, the State Office of Criminal Investigations were still deciding whether or not to investigate the matter further.
The two neo-Nazis – both from Berlin's Neukölln district – are already known by police to be violent right-wing criminals, reports Berliner Zeitung.
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They are already on police records for robbery, theft, serious bodily harm, coercion and identifying themselves as part of anti-constitutional organisations.
Police investigators have appealed for the family to come forward, encouraging them to call 030/297779-0 or get in touch with any other police station.