The Federal Supreme Court - the top arbiter in civil cases - has ordered a trusteeship to be set up in order to establish the father's identity, according to 20 Minutes.
Putting the ruling into practice could prove difficult, though, due to the mother's resistance.
This kind of trusteeship is usually used when it is necessary to ensure sufficient payments for the child's maintenance and education are received.
But the woman in this case, from the Fribourg region of the country, argues that she doesn't require any financial assistance from the child's father because she earns enough to live "comfortably". She added that she has "personal reasons" for concealing his name.
Judges disputed her claims, saying that due to the fact she only works part-time, her salary could not be considered "particularly comfortable".
The mother even argued that the revelation of his identity may have "destructive social and psychological disadvantages."
She said that her daughter, currently just over one year old, could decide for herself if she wanted to know who her father was once she reached the age of 19.
However, the tribunal rejected the argument that the mother's privacy was being violated.
The cantonal court argued that it is unfair to make the girl wait until adulthood before finding out who her father is, because she would miss out on "the benefit of establishing a paternal link during her childhood and adolescence, important phases in her development. "