Police made the discovery after being called to the apartment in the San Giovanni area earlier this week.
Concerned neighbours had alerted the authorities after they hadn't seen or heard from the two frail women in a few days, Corriere Della Sera reported.
Police eventually managed to enter the apartment and found the two women, aged 93 and 80, both collapsed on the floor – dehydrated and lacking the strength to get up or call for help.
Both were immediately taken to hospital, where the 93-year-old sister died on Tuesday.
Police searched the apartment - described as having "terrible hygienic conditions" - to find the contact details of a possible next of kin, but could only find wads of cash stuffed inside a pair of canvas bags, which amounted to almost €100,000 in banknotes of €50.
More money and other valuables were found elsewhere in the house, bringing the total worth to €200,000.
Police suspect that the hoard represents the life savings of the pair but are still investigating and trying to locate a next of kin.
Strangely, all of the banknotes were crisp and fresh, suggesting that the decision to store the cash at home had been made recently.
The surviving 80-year-old sister is still in hospital but said to be "in a confused state".
For the meantime, police have sequestered the home, while the hoard has been placed in a bank on her behalf by a trustee.