Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
Whisk together the flour, sugar, baking powder, and salt. Add the butter and mix with a fork, a pastry blender, or your hands.
Stir in the sour cream. Stir in the milk. Dough will be sticky. Gently stir in the blueberries, trying not to break any of the berries. (If a few break, it's absolutely fine.)
Drop the dough by roughly 3 tablespoons onto the prepared pan. Bake for 20 to 25 minutes, or until the biscuits are lightly browned and feel set when lightly tapped on top.