The court found local courts had discriminated against the woman, born in 1967 in the United States to a Jewish father and a US mother, who were unmarried.
Article 116 (2) of Germany's constitution - known as the Basic Law - states that Germans who between 1933 and 1945 were stripped of their citizenship on political, racial or religious grounds and their descendants can have their citizenship back.
The court ruling, dated May 20 and made public on Wednesday, stated that children born out of wedlock to former German citizens are equally entitled to citizenship.
The decision opens the door for descendants of German Jews born outside marriages to become German citizens.
"If a law mandates the state to grant citizenship, this right must be fulfilled without discrimination against illegitimate children," the court said.
Jewish campaigners said it was a "momentous judgment."
Nicholas Courtman of the Article 116 Exclusions Group said it would have "wide-ranging consequences for the naturalization rights of descendants of German citizens persecuted under National Socialism."
Germany last year enforced two decrees to make it easier for people, mainly Jews, who fled Hitler's Nazi regime because of persecution as well as their descendants to have their citizenship restored.
The decrees followed a campaign by descendants of refugees from Nazi Germany who are angry that their applications for citizenship have been rejected despite constitutional guarantees.
Last year's decrees loosened the conditions needed for citizenship, for example by allowing individuals with a German mother and foreign father to have their citizenship restored, provided they were born before April 1953.The new ruling said fathers should be able to pass their citizenship to their children too, not only mothers.