Using the small holes of a box grater, grate the cucumber. Transfer the grated cucumber to a few layers of paper towels (or cheese cloth) and squeeze out the excess water. Add the shredded cucumber to a small mixing bowl.
Add the yoghurt, garlic, parsley and olive oil to the bowl. Stir until well combined. Season generously with salt and pepper. Mix and taste to adjust for seasoning.
Cover with plastic wrap or transfer to an airtight container and refrigerate for at least one hour before serving.