Grate the cucumber using the large holes of a box grater.
Place the grated cucumber in a clean kitchen towel or cheesecloth and squeeze firmly to remove as much liquid as possible.
In a medium mixing bowl, combine the Greek yogurt, minced garlic, olive oil, and lemon juice.
Fold the drained cucumber and chopped dill into the yogurt mixture.
Season with salt and black pepper, stirring until fully incorporated.
Cover and refrigerate for at least 30 minutes before serving to allow the flavors to develop.