The €500 (£440; $600) notes were cut up and found in the toilets of a branch of the bank UBS and in three nearby restaurants.
Thousands of francs have reportedly been spent on plumbing repairs to unclog the surrounding pipes.
The high-value euro notes are due to be withdrawn in 2018 over fears they facilitate illegal activities.
They will remain legal tender, but the European Central Bank will stop producing them following a European Commission inquiry into their use.
Destroying notes is not an offence in Switzerland, but local prosecutors confirmed they were looking into the circumstances around the unusual find.
"We're trying to find out where the notes came from and whether a crime has been committed," Vincent Derouand from the Geneva prosecutor's office told the BBC.
"Clearly it's very surprising," he said.
Mr Derouand would not comment on local reports (in French) that a lawyer had been questioned in relation to their enquiries.
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