The Frenchwoman took the 50,000 francs ($48,600) cash to the nearest police station, according to the report in 20 Minutes.
Speaking to the paper, a Basel police spokesman said the owner of the cash is invited to come forward but must “prove that it belongs to them”.
Consequently, police will give out no details of the type of notes or the envelope within which the cash was found.
As is usual in cases like these, the woman who handed in the cash should get a reward of ten percent of the total amount found.
If the owner does not come forward within a year, she can keep the total sum, said the spokesman. However she would be advised not to spend it all straight away; under Swiss law the owner has five years to claim it back.
The news comes just days after a pensioner handed in nearly 6,000 francs he found on the street in Zurich.
And earlier this year a tram driver in Basel found a bag containing 144,000 francs on his tram.
However the cash was quickly reunited with its owners, a couple in the city to visit their daughter, since the bag also contained their identity documents.