Preheat your oven to 350°F (175°C). Grease a muffin tin or line with muffin liners.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, mix the grated zucchini, vegetable oil, vanilla extract, and non-dairy milk.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.