The 19-year-old woman had approached the baby's 35-year-old mother while she was grocery shopping with her three children on Thursday afternoon, police report.
The younger woman offered to take care of the mother's four-month-old baby girl, who was in a carriage, while the mother brought her groceries into her flat.
When the mother returned, her baby and the woman had disappeared. The mother then called the police, who launched an extensive search with dogs, helicopters and emergency officers.
Police eventually found that the 19-year-old had fled to Lower Saxony with the baby - around 250 kilometres away from Potsdam.
Several hours later at around 8pm on Thursday, the woman was arrested in Hanover, police reported. The baby was found unharmed.
Due to organizational complications, however, the mother could not be reunited with her baby until Friday morning, a police spokesman said.
Police also reported that the 19-year-old had acted alone and did not make any demands.
Investigators so far do not believe that the woman and mother knew each other previously, and the motive behind the crime thus far remains unclear.