Combine blueberries and sugar in a saucepan over medium heat; cook and stir until sugar has dissolved, about 5 minutes. Transfer syrup to a covered container and freeze for 30 to 40 minutes.
Stir coconut milk into syrup until uniform. Pour into an ice cream maker; freeze according to manufacturer's instructions, about 20 minutes. Transfer to an airtight container and freeze until firm, about 4 hours.