Preheat oven to 180°C. Grease or line a 12-cup muffin tin.
Grate carrot until you have 1 cup worth. Add to a large bowl with milk, eggs and oil and stir to combine. Add muffin mix and fold to combine.
Divide batter between muffin cups and bake for 25-30 minutes, until a knife inserted comes out clean.
Whisk together icing ingredients until smooth. Wait for muffins to cool completely before icing.