Preheat the oven to 350°. Line an 8½x4½" loaf pan, preferably metal, with parchment paper, leaving an overhang on the long sides, and lightly coat with non-stick spray.
Whisk flour, baking powder, and salt in a medium bowl.
Work grapefruit zest into granulated sugar (I used my Kitchen Aid mixer to do this) in a large bowl until sugar starts to clump and the mixture is very fragrant about 1 minute.
Add eggs, oil, and vanilla and beat with an electric mixer on high speed until light and thick, about 4 minutes. Reduce speed to low and mix in half of the dry ingredients, then mix in ¾ cup yogurt. Mix in remaining dry ingredients followed by 4 Tbsp. grapefruit juice and 1 Tbsp. poppy seeds.
Scrape batter into prepared pan and smooth top.
Bake loaf until the top is golden brown and a tester inserted into the center comes out clean, 50–60 minutes. Transfer pan to a wire rack. Poke holes on the top of the cake and brush 3 Tbsp. grapefruit juice over top. Let sit 15 minutes, then run a knife around the sides to loosen and use parchment paper to lift the cake out of the pan and onto the rack. Remove parchment and let cool completely.
Whisk powdered sugar, remaining 1 Tbsp. yogurt, 1 tsp. grapefruit juice in a medium bowl until smooth and drizzle over cake. Let sit until glaze is set, about 30 minutes.