Ms Raunigk, who is in the 21st week of her pregnancy, said she was "shocked" when an ultrasound scan showed she was carrying quadruplets.
Her gynaecologist initially mentioned the possibility of a "selective reduction", where one or more fetuses is aborted in a multi-fetal pregnancy, but she declined.
But the English and Russian teacher, who is due to retire this year, said she decided to have the babies as she was "still quite fit" and capable of looking after them.
She added: "I don't think I will have any problems."
Ms Raunigk, from Berlin, previously made headlines in Germany when she had her daughter Leila at the age of 55.
She told German media that she does not worry about what her future will look like in five years time, with a teenage daughter and the young quadruplets, as she assumes she will "stay healthy".
Her 13 children - the oldest of whom is 44 - are by five different fathers, and Ms Raunigk has seven grandchildren.
She defended her decisions to get pregnant later in life, saying: "I think one needs to decide for oneself and not listen too much to the opinions of others."
At present, the oldest woman to have given birth to quads is Merryl Fudel, who was 55 at the time.
The oldest woman ever to give birth is Indian Omkari Panwar, who was believed to be 70.
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