Preheat the oven to 400 degrees F (200 degrees C). Coat a large baking sheet with cooking spray.
Combine chicken, feta cheese, egg, bread crumbs, carrot, celery, garlic, and ranch dressing mix in a large bowl. Mix evenly until combined. Form mixture into 1/2-inch meatballs and place on the prepared baking sheet.
Bake in the preheated oven for 10 minutes; turn meatballs. Continue baking until no cooked through, about 14 minutes more.
Transfer cooked meatballs to a large bowl, add Buffalo wing sauce, and gently toss to combine.