Place garlic in a mortar; season with salt and pound to a very fine paste. (Alternatively, place garlic on a cutting board, season with salt, and mash with the side of a chef's knife.) Transfer garlic paste to a small bowl and gradually whisk in oil.
Very gradually whisk yogurt into garlic mixture until emulsified. (Add too fast and sauce will break. If it does break, gradually whisk in 1 teaspoon water just before serving.)
Do ahead: Garlic sauce can be made 6 hours ahead. Cover and chill.