Portraits of Robert Mapplethorpe, Jean-Michel Basquiat, Keith Haring, Bianca Jagger and other influencers are now on view at the Collezione Maramotti.
Shiseido fragrance arm will create and distribute perfumes for the French brand.
The Milan installation was set up to highlight and condemn the increasing violence against women.
The apparel firm said it intends to use the proceeds of the offering for general corporate purposes, which may include acquisitions.
The beauty entrepreneur died Monday at her home in Beverly Hills.