Place the shredded carrots in a small pot and cover with water. Bring to a boil and keep at a low boil for 5 minutes. Drain and rinse under cold water until cooled.
Place the sectioned grapefruit in a blender, followed by the cooked carrots, yogurt, squeezed juice from both grapefruit halves, ice cubes, and sugar. Blend until completely smooth. Serve cold.