The unknown man offered the girl a paper cup containing the German spirit Schnaps at the market near Berlin's Alexanderplatz. After drinking it, she vomited and suffered short-term memory loss.
Doctors confirmed that a substance, not yet identified, had been mixed into the drink.
It is unclear whether the poisoner was the same man who poisoned at least seven people in various Christmas markets around Berlin this week.
The man was first seen at a market in the capital's Charlottenburg district, where he told two foreign visitors he was a new father and wanted to celebrate by offering them free drinks of alcohol, Der Tagesspiegel newspaper reported on Friday.
Police said the victims may have been given a mixture of alcohol and so-called “knockout drops” meant to render people unconscious so they can be robbed or sexually assaulted.
Police are now searching for a slim man in his mid-40s, about 1.8 metres tall with short, dark blond hair.