Dr Williams's Theological Library in London, which is hoping the proceeds from the sale, which are estimated to be more than £3m, is selling the book.
No collected edition of Shakespeare's plays was ever published during the playwright's lifetime and it is likely that they survive only because of their inclusion in the book and would otherwise have been lost.
The folio is bound in brown leather and is full of annotations, marking significant parts of the text.
The director of Dr Williams's Theological Library, Dr David Wykes, said: "The library has been proud to own this remarkable copy of Shakespeare's first folio.
"Its sale will secure the finances of the library and safeguard our important historical collections of manuscripts and printed books for future generations."
The book will be displayed at Sotheby's offices in London, Chicago, Los Angeles, New York, Beijing and Hong Kong in April and May, before the auction, which takes place on 13 July.
