The measure, dubbed the 'milkmen's kids law' in the media, is to pass the cabinet as early as Wednesday before heading to parliament.
It would apply to cases in which men who believe they are not the real fathers seek financial compensation in court.
"We need to offer more legal protection for 'false' fathers to seek recourse," Maas said.
"The mother should only have the right to remain silent when there are serious reasons for her not to name the biological father."
A court would determine if the reasons sufficed for her to keep the father's true name a secret.
The measure would allow men who were duped into paying to support a child to demand compensation from the biological father for a period of up to two years.
Maas began work on the legislation after a federal court ruling in February 2015 said the government needed to put men tricked into believing they were fathers on firmer legal footing.
Opinions vary on how many children grow up thinking the wrong man is their father but German studies put the figure from below four percent to more than 10 percent.
It was not immediately clear what penalties a woman who refused to unmask the biological father would face.