In a small saucepan, bring the sugar, water, and ginger to a boil over high heat, stirring to dissolve the sugar, about 5 minutes. Remove from the heat, add the mint leaves, stir to combine, and let cool to room temperature, about 1 hour. Place a fine-mesh strainer over a 1-1/2- to 2-quart container and strain the syrup, discarding the solids.