Preheat oven to 350°F (175°C) and line or grease a 12-cup muffin tin.
Whisk together flour, baking soda, baking powder, salt, and cinnamon in a large mixing bowl.
In a separate bowl, whisk together applesauce, maple syrup, egg, and vanilla until smooth.
Grate the zucchini and press with a clean towel to remove excess liquid until approximately 1 cup of dry mass remains.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the squeezed zucchini and walnuts.
Divide batter evenly into the 12 muffin cups.
Bake for 20 to 24 minutes until a toothpick inserted into the center comes out clean.
Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.