Preheat oven to 180 degrees C. Grease 12 muffin cups or line with paper muffin liners.
Whisk the flour, salt, baking powder, matcha and sugar together in a mixing bowl; set aside. Whisk together the egg, melted butter and milk in another bowl. Stir the milk mixture into the flour mixture until just moistened. Stir in walnuts. Divide the batter among the prepared muffin cups.
Bake in the preheated oven until golden and the tops spring back when lightly pressed, about 25 minutes. Cool in the muffin tin for 5 minutes then remove to cool on a wire rack.