The woman, Annegret Raunigk, already has 13 children.
The quadruplets – three boys and a girl – were born prematurely at 26 weeks in a Berlin hospital but have “good chances of surviving”, according to the entertainment channel RTL, which has negotiated exclusive rights to the woman’s story.
Raunigk lives in Berlin and is an English and Russian teacher who is close to retirement.
In addition to her children, she has seven grandchildren.
RTL said the new arrivals make her the world’s oldest mother of quadruplets. The boys have been named Dries, Bence and Fjonn and the girl Neeta.
Raunigk made headlines 10 years ago when she gave birth to her 13th child, Lelia, at the age of 55.