Preheat oven to 350°F (175°C). Grease a muffin tin or line with paper liners.
In a large bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon.
In another bowl, mix sugar, oil, eggs, and vanilla until well combined. Stir in grated zucchini and carrot.
Add the wet ingredients to the dry ingredients and mix until just combined.
Spoon the batter into the prepared muffin tin, filling each cup about ⅔ full.
Bake for 20 minutes or until a toothpick inserted into the center comes out clean.
Let cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.