Preheat your oven to 350°F (175°C). Grease a cake pan.
In a mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, combine the Greek yogurt, vegetable oil, eggs, grapefruit zest, grapefruit juice, and vanilla extract.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.