Whisk yogurt, sugar, and salt together in a mixing bowl until sugar has completely dissolved. Chill in an ice bath or refrigerate until yogurt registers at least 45°F (7°C) on an instant-read thermometer.
Churn yogurt in ice cream machine according to manufacturer's instructions. Transfer yogurt to airtight container and chill in freezer for at least 4 to 5 hours before serving.
