Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners.
In a large bowl, combine the grated zucchini, Greek yogurt, sugar, vegetable oil, eggs, and vanilla extract. Mix until everything is well blended.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
Slowly add the dry ingredients to the wet ingredients, stirring gently until just combined.
Spoon the batter into the muffin cups, filling each about two-thirds full.
Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.