A statement released by the police and state prosecutors said a male acquaintance had found the body parts of the infants while trying to clear out the flat of the dead woman this week.
"The cause of death is currently not known," the police said, adding they would perform an autopsy.
In recent years there have been a number of high-profile cases of infanticide in Germany, with the most notorious involving a woman jailed for 15 years in 2006 for the manslaughter of eight babies.
Sabine Hilschenz, a divorced, unemployed and alcoholic dental assistant from a depressed area of the ex-communist east of the country, hid the corpses in buckets, flowerpots and an old fish tank at her parents' home.
The Berliner Morgenpost on Friday reported there seemed to be parallels to that case in the latest incident, except that the 46-year-old mother lived in a 18-storey building in a more affluent part of western Berlin.
“We live in a bourgeois area, the apartments aren't cheap, and the residents are from the appropriate circles,” a male neighbour told the paper. “I'd never have imagined something like this could happen.”
Another resident questioned how the babies had only now been found.
“After the woman took her life we had a bunch of police. They were in the flat too,” she said. “How could they not have found the remains then?”