Police launched a probe into possible human trafficking after they were tipped off about the advertisement which appeared online on Tuesday.
The 40-day-old girl has been handed to child protection officers, police from the western city of Duisburg said in a statement.
Preliminary investigations show that the advertisement was put up using the internet connection of the couple, identified by police only as "refugees".
However, police said the internet connection was also in use by other members of the family, adding that the probe was ongoing.