Preheat the oven to 350 degrees F (175 degrees C).
Combine oats, whole wheat flour, brown sugar, cinnamon, baking powder, and baking soda in a large bowl. Stir in peanut butter, margarine, and egg. Add shredded zucchini and mix thoroughly.
Drop spoonfuls of cookie dough onto ungreased cookie sheets.
Bake in the preheated oven until edges are lightly browned, about 12 minutes. Cool for 3 minutes before transferring to wire racks.
