Preheat oven to 400 degrees F (200 degrees C). Spray 12 muffin cups with cooking spray.
Combine flour, cocoa powder, baking powder, and cinnamon together in a bowl. Stir beets, applesauce, oil, honey, and egg together in a separate bowl; stir into flour mixture just until batter is combined. Spoon batter into the prepared muffin cups.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 18 minutes. Remove muffins from tin immediately.