Cut off the top and the bottom of the melon. Set the melon upright on 1 of the cut sides. Using a smooth stroking action from the top of the melon to the bottom, let your knife peel off the outer layer. When the entire melon is peeled, quarter the melon by cutting it from top to bottom. Scoop out the seeds and cut each 1/4 into 5 slices; cut the slices in 1/2.
Cut each slice of prosciutto into 3 pieces and wrap the middle of each melon slice with the prosciutto. Arrange on a platter.