Simmer the water, cranberries, and sugar in a small saucepan set over medium-high heat until the berries begin to pop, approximately 7 minutes.
Remove from the heat. Puree with an immersion blender, conventional blender, or food processor for 1 minute. Pass the mixture through a fine-mesh strainer directly into a metal 9-by-13-inch pan. Do not press on the skins; simply allow the juice to drip through the strainer. Add the zest and stir to combine.
Freeze until set, at least 6 hours or up to overnight. Once frozen, scrape the mixture with a fork to create a shaved ice texture.