The sum, in €50 notes stuffed into two plastic bags, was found under the priest's seat in the confessional, where it had been left sometime this week.
Staff at the church, which lies a few hundred metres south of the Vatican in the west of Rome, immediately reported the find to the carabinieri, who are now checking the serial numbers as they investigate where the money came from.
"There are some details that are raising doubts," Lieutenant Salvatore Friano told the press.
"We can say that it is not fresh money. We're also going to look at surveillance camera footage to try and find out whether this was a benefactor who wanted to donate this money to the church, or someone who wanted to get rid of it."
The Church of Santa Marai delle Grazie all Fornaci. Photo: Croberto68/Wikimedia
The concern is that the banknotes could be illicit gains dumped in the church by a criminal (even a repentant one).
"Of course such a sum would be handy for the parish, but not to someone else's detriment," said Father Giovanni Martire Savina, who was the first to open the bags.
The church has received generous donations of up to €1,000 in the past, he added, "but never anything like this".
If the cash is found to be ill-gotten, it will be confiscated by the state; if the money's clean, police will seek to track down the person who left it to establish whether they meant to leave it behind or simply forgot it.
At which point they'll have the option to re-donate it in a more traditional manner, should they so choose.
- Bernini masterpiece loses a finger on its way back to Rome church
- Italy's art police recover works stolen from quake-hit churches
- Losing faith: why Italians are spurning the Church