Preheat oven to 350 degrees F (175 degrees C). Press pie crust into a 9-inch pie pan.
Mix sweet potatoes, sugar, butter, milk, eggs, vanilla extract, nutmeg, and cinnamon together in a bowl; pour sweet potato mixture into the prepared pie crust.
Bake in the preheated oven until a knife inserted near the center comes out clean, about 1 hour.