They made the grim discovery after being called out to investigate a "strong smell" emanating from the bowels of the building in Oulu, northwest Finland.
The woman turned herself in and said the bodies were those of three stillborn babies she had given birth to between five and 10 years ago, a police statement said.
She was unable to explain the discrepancy in the number of bodies.
Police said the precise age of the infants could not be established, but they appeared to be "foetuses nearing maturity whose death dates back several years".
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Seppo Leinonen, a police officer interviewed on public television station YLE, said the foetuses "were developed enough to assume that if they were born in a normal way they would have survived."
He added that the woman was employed and has other living children.
A neighbour quoted by the Finnish tabloid Ilta-Sanomat said the woman worked in the catering industry.
According to YLE, relatives of the woman were not aware of her secret and were "shocked" by the discovery.