Preheat the oven to 350 degrees. Lightly grease a loaf pan.
To remove the grated zucchini of excess moisture, place the zucchini on a layer of paper towels, wrap the towels around the zucchini, and squeeze firmly over the sink. Set aside.
In a large bowl, whisk the egg. Add the bananas and mash together until large banana lumps are smooth.
Stir in the yogurt, sugar, and vanilla extract until smooth.
Sprinkle in the baking powder, baking soda, salt, and ground cinnamon and stir until smooth.
Sprinkle in the flour and fold until just combined. Add the zucchini and fold until just combined.
Pour into your prepared loaf pan and bake for 55-60 minutes, until the top is golden brown and a toothpick inserted into the center comes out clean.