Their 44 year-old mother, whose name has not been disclosed, was arrested on suspicion of killing the newborn babies, presumably in the late 1980s as one of the bodies was wrapped in a newspaper dated 1988.
The woman is married to a 47 year-old electrician and has two sons, aged 18 and 22, and a 24 year-old daughter. Neighbors describe the family as reserved, but friendly in television interviews.
The mother was driven to the police station by her family after two of her children came across the gruesome findings while looking for something to eat in the basement fridge.
The forensic team ruled out the possibility that the babies were stillborn, but it is still unclear whether they were breathing when put into the freezer. Autopsies to establish the cause of death will be carried out as soon as the bodies are thawed.
According to preliminary reports, the woman was able to easily conceal the three pregnancies from her family as she was overweight. She subsequently delivered the babies in the bathroom of her home and put them in plastic bags so that they suffocated.
"The crime is basically solved," the Deutsche Press Agency cited a prosecutor as saying.
The mother, who says she feels "deeply guilty," is currently undergoing psychiatric care and will be questioned later.
Germany has been shocked by a series of infanticides in recent years leading to many clinics to introduce hatches where unwanted babies can be left anonymously in an attempt to save lives.
In the most notorious case a 40 year-old alcoholic, Sabine Hilschenz, was jailed for 15 years for letting nine of her newborn babies die and hiding their remains in buckets, flower pots and an old fish tank around her home.
In December 2007 German police arrested a 31-year-old woman who gave sleeping pills to her five children aged between three and nine, subsequently suffocating them with plastic bags near the northern city of Kiel. The same week, a woman in Plauen, eastern Germany, was detained after three dead newborn babies were found in her cellar, balcony and fridge.