Combine the sugar, water, and ginger in a medium saucepan over medium heat, stirring occasionally until the sugar dissolves. Simmer over very low heat for 5 minutes, then remove from the heat and stir in the mint leaves. Cover and allow to steep until syrup is cool. Strain through a fine-mesh sieve, pressing to release as much syrup as possible; discard solids. Transfer syrup to a clean bottle or other lidded container.

Syrup may be refrigerated for up to 1 month.