PARIS—Christian Dior started dismissal procedures against designer John Galliano for making "deeply offensive" anti-Semitic remarks, acting fast to distance itself from a potentially damaging association with a couturier whose star was already starting to fade.

On Friday, Dior had suspended the 50-year-old Mr. Galliano, one of the fashion industry's most celebrated rags- to-riches tales, after the designer was questioned by police for allegedly making anti-Semitic slurs to a couple during a late-night row in a trendy Paris...