In a mixing bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk together milk, egg, and melted butter.
Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the grated apple.
Heat a griddle or skillet over medium heat and lightly grease it. Pour ¼ cup of batter for each pancake onto the griddle.
Cook until bubbles form on the surface of the pancakes and the edges look set, about 2-3 minutes. Flip and cook until golden brown on the other side, about 1-2 minutes more.