Justice Minister Sabine Leutheusser-Schnarrenberger, who drew up the bill, said she hoped the new law would encourage "fathers to take responsibility for their child."
A copy of the draft bill, leaked to the Süddeutsche Zeitung, said it was designed to make it significantly easier for unmarried fathers to apply for joint custody, even if the mother does not want contact with him.
The new bill is a response to a Constitutional Court ruling from 2010, which said that the current law, allowing joint custody only with the mother's agreement, is unconstitutional. This followed a verdict from the European Court of Human Rights in Strasbourg, which said that the German law denied single fathers a basic human right.
Leutheusser-Schnarrenberger's new proposal grants the unmarried mother automatic custody of her child, but allows the father the right to apply for joint custody at any time. This application is forwarded to the mother, and if she does not object, joint custody is to be granted with as little bureaucracy as possible.
If she does object, she must provide reasons why joint custody would put the child's well-being at risk. These are then examined by a court, which has the power to deny the father custody if necessary.
If her reasons are not recognizably related to the child's well-being, the mother's objections can be rejected - this would include, for instance, that she only had a brief relationship with the father and does not want further contact.
Leutheusser-Schnarrenberger's bill is supported by social science research that suggests children generally want to have a close relationship to both parents.
The new proposal is also a reaction to rapidly changing family structures in Germany - the percentage of German children born out of wedlock has doubled since 1995, and now stands at around 33 percent.
What the proposal does not include though, is a suggestion made by some social scientists that parents should automatically gain joint custody if they live together. Studies suggest that co-habiting unmarried parents cooperate particularly well in raising a child, but the Justice Ministry argued that it would be difficult to prove that the parents co-habit in individual cases.