Mix flour, sugar, salt, and baking powder together in a large bowl. Mix yogurt, egg, water, and vanilla extract together in a small bowl. Pour yogurt mixture into flour mixture; mix until well incorporated. Add additional water by the tablespoon if needed to reach the right consistency.

Heat oil in a griddle or skillet over medium heat. Use approximately 1/4 cup of batter per pancake. Cook until golden brown, 2 to 3 minutes per side.