The attack happened in the early hours of Monday, police said in a report.
The woman was found by police at a bus stop in the Rotthausen area of Gelsenkirchen, a city in North Rhine-Westphalia.
She had approached a passer-by for help because she could not find her way home. The passer-by alerted the police over fears for the woman.
When the police arrived, they found the 42-year-old woman's face and shaved head had been smeared with permanent markers.
In addition to a moustache and painted crowns above her eyebrows, there were 10 swastikas on her scalp, police said.
The woman said that she had gone to an apartment with two unknown women the night before to drink beer together.
She had then probably fallen asleep at some point, and when she woke up she wanted to go home but was disorientated.
Police said that the victim was unaware that she was covered in permanent marker.
Officers also found that the woman's upper body had been urinated on. She was unable to provide further information on what happened.
In a statement police said: “Officers took the Gelsenkirchen woman to the station to preserve evidence and further clarify the facts of the case.”
The woman was taken home after evidence had been gathered. Police have launched a probe and investigations are continuing.
The swastika and other Nazi symbols are banned in Germany. Those caught breaking the law can be fined or face a jail term of up to three years.