"It is with great sadness that I announce the passing of Pierre Godé," Arnault said in a statement issued by LVMH.
"Alongside my father, Jean Arnault, and then alongside me, Pierre Godé was instrumental in the creation and growth of the LVMH Group. His lively intelligence and sound judgment will be missed by all who came to know and appreciate him."
Despite his ill-health, Godé remained an advisory member of the LVMH and Dior boards.
A lawyer by training, Godé worked alongside Bernard Arnault from the mid-1980s to build up LVMH, now the world's largest luxury group, with brands ranging from Dom Perignon champagne to fashion houses Fendi and Givenchy.
As well as advising Dior and serving as a vice-chairman of LVMH, Godé was on the board of media and advertising group Havas and a member of France's Competition Authority.
By Dominique Vidalon; editor: David Goodman.