Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Meanwhile, heat oil in a large skillet over medium heat. Saute garlic until it starts to brown. Stir in a handful of grated zucchini; cook for 1 minute and then add the rest of the zucchini. Cook for 3 minutes.
Toss pasta with zucchini, cheese and yogurt. Season with salt and pepper. Mix well and serve.