Place the strawberries, sugar, and water in a medium saucepan. Starting on medium heat, bring the fruit mixture to a boil, and then reduce to a simmer for roughly 15 minutes. With a wooden spoon, occasionally mash the strawberries to release the juices.

Using a mesh strainer, strain the mixture into a bowl, and let it cool. Once cool, add the strawberry liquid into the bottom of a large jar or pitcher. Add the milk and stir to fully combine. Serve cold.