This list of books has not always excelled at identifying work by female writers, but in Switzerland, which only gave women the vote in my lifetime, they do rather well. The most popular "switzerland"-tagged book on both LibraryThing and Goodreads probably has to be disqualified in that not enough of it is set there - parts of the plot take place in Germany, Ireland and the Arctic wastes - but the most memorable passages are indeed set in the vicinity of Lake Geneva, where it was written by an eighteen-year-old writer in the summer of 1816, and later published in 1818. Brian Aldiss argues that it is the first true work of science fiction. It is of course:
Frankenstein: Or the Modern Prometheus, by Mary Wollstonecraft Shelley
There is a better answer, in the shape of a book by a Swiss woman which has become identifued with Swiss girlhood (though in fact the second quarter of it is set in Frankfurt, which I had completely forgotten). Published in 1880, and apparently dashed off by its author in four weeks, it's the story of a little girl bringing joy to her grumpy grandfather in the Grisons, though there's also stuff going on about poverty and disability. It is of curse:
Heidi, by Johanna Spyri
I'm happy enough with a book that is 75% set in Switzerland. If you prefer a book that is almost 100% set in Switzerland, we can stay in the Grisons, but I'm afraid I must refer you to a male German writer. His masterwork, published in 1924, deals with illness, philosophy, and death. It is:
The Magic Mountain, by Thomas Mann
This has been a more highbrow entry than some!