Preheat the oven to 350°F (175°C).
Grease an 11×7-inch baking dish.
In a large bowl, combine the stuffing mix and melted butter; stir well.
Reserve 1/2 cup of the stuffing mix for topping.
Add zucchini, chicken, soup, grated carrot, onion, and sour cream to the remaining stuffing in the bowl; mix thoroughly.
Transfer mixture to the prepared baking dish and spread evenly.
Sprinkle the reserved stuffing mix over the top.
Bake for 40 to 45 minutes until bubbly and golden brown.
Remove from oven and let cool slightly before serving.