Preheat oven to 350°F (175°C). Place butter in an 8-inch square baking dish.
Melt butter in the preheating oven, about 5 minutes. Remove from oven.
Mix flour, sugar, and milk in a bowl until combined; pour batter over melted butter. Scatter blueberries over batter.
Bake in preheated oven until a toothpick inserted into the center comes out clean, about 1 hour.