Grease and flour a 9-inch bundt cake pan and preheat the oven to 325 F.
Beat the cream cheese and oil with a hand-held or stand mixer until creamy.
Add the cake mix, pudding mix, eggs, lemon zest, and vanilla extract, and beat until smooth.
Fold in the blueberries and spoon the batter into the pan.
Bake for 60-65 mins or until a toothpick inserted in the middle comes out clean.
Cook in the pan for 10 mins, then unmold and cool in a wire rack.
While the cake is cooling, make the icing by combining the milk with the confectioner's sugar.
Drizzle the icing over the cooled cake and serve.