A remedy that contains a small amount of whatever caused the ailment: “When Anne had a bad hangover, Paul offered her a Bloody Mary and said, ‘Have a little of the hair of the dog that bit you.’”
Whatever made you ill used as a remedy, especially alcohol as a hangover cure. For example, A little hair of the dog will cure that hangover in no time. This expression, already a proverb in John Heywood’s 1546 compendium, is based on the ancient folk treatment for dogbite of putting a burnt hair of the dog on the wound. It is often shortened, as in the example.