The 28-year-old woman is said to have given birth to the babies in secret – and then killed them, all without the knowledge of her husband.
The police in Flensburg, near the border with Denmark, said the woman was married with two children aged eight and ten.
The family lived at a “certain level of prosperity” and she was scared of being unable to maintain their standard of living if she had more children, the prosecutor said. Her husband did not want more children, yet contraception was “never a topic” for the couple, she said.
He is said to be deeply shocked and receiving counselling.
“The accused has made a complete confession to the police,” said prosecutor Ulrike Stahlmann-Liebelt. Two children were killed in 2006 and 2007 – and three more after that.
She gave birth to two of the babies at home – and three in the woods, alone.
The police said no-one had known of her pregnancies, not even her husband. They said the discovery and her confession were likely to have prevented further cases.
The body of one child was found in the recycled paper facility in 2006 in Ahrenshöft near the family's home in the Husum area of northern Germany.
A post mortem examination showed the baby had lived for a short time after it was born, while a report from NDR public broadcaster suggested the placenta was also found, from which a DNA sample of the mother was retrieved.
The second baby was found by a driver a year later, wrapped in a plastic bag and dumped in a parking space near a major rural road. The police have been carrying out DNA testing of women in the region since then, and got a match with this woman, who then confessed to killing not only the first two babies but three more.
The three other bodies were stashed in cardboard boxes in the family cellar. They were so badly decomposed that no time of death or cause of death could be determined.