In a small saucepan, combine the water, sugar, and ginger and simmer over moderate heat, stirring occasionally, for 1 minute. Stir in the Campari. Cool and set aside.
Cut the peel and the bitter white pith from the grapefruit with a sharp knife. Working over a bowl to catch the juice, cut the grapefruit sections free from the membranes, keeping sections intact. Place in a medium bowl. Reserve the juice. Strain the Campari syrup and pour it and the reserved juice over the grapefruit sections. Cover and chill. Recipe can be made up to 1 day ahead.