Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt.
In another bowl, combine the grated zucchini, granulated sugar, brown sugar, vegetable oil, egg, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups, filling each about 3/4 full.
Bake for 20-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the tin for 5 minutes before transferring to a wire rack to cool completely.