Preheat oven to 375 degrees F (190 degrees C). Grease an 8x8-inch baking pan. Grease 15 muffin cups or line with paper muffin liners.
Combine water and corn bread mix in a bowl; stir until smooth. Pour batter into 8x8-inch baking pan.
Bake in the preheated oven until top is golden brown, 30 to 35 minutes. Remove from oven; reduce temperature to 350 degrees F (175 degrees C). Cool corn bread until easily touched, about 15 minutes.
Melt butter in a skillet over medium heat. Stir onion and celery into the skillet; cook and stir until vegetables are firm yet tender, 5 to 7 minutes. Remove from heat; cool.
Crumble cooled cornbread into a large bowl. Stir in stuffing mix and poultry seasoning; mix until well combined.
Stir eggs into the cooled vegetable mixture; pour immediately into cornbread mixture. Stir until well mixed. Pour in chicken broth; stir until ingredients stick together. Form mixture into palm-size balls; place into prepared muffin cups.
Bake in preheated oven until tops spring back when lightly pressed, about 35 minutes.