With the rack in the middle position, preheat the oven to 350°F (180°C). Line a 12-cup muffin tin with paper or silicone liners.
In a bowl, combine the flour, sugar, cocoa powder, baking soda, baking powder and salt. Add the water, mayonnaise and vanilla. Mix with a spoon until smooth. Divide the batter among the muffin cups, about ¼ cup (60 ml) of batter per muffin.
Bake for 17 to 20 minutes or until a toothpick inserted in the centre of a muffin comes out clean. Let cool on a wire rack.
In a bowl, beat all of the ingredients with an electric mixer for 2 to 3 minutes or until smooth and airy.
Using a butter knife, spread the icing over the cooled cupcakes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.