Whisk buttermilk, Buffalo sauce, mustard, garlic, salt, and pepper together in a shallow bowl. Add chicken. Cover and marinate in the refrigerator for 12 to 24 hours.

Preheat the oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish.

Pour chicken and marinade into the prepared baking dish.

Bake in the preheated oven until juices run clear, about 40 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).