Place rhubarb in a saucepan with enough water to cover; bring to a boil. Reduce heat to medium, cover, and cook until tender, about 10 minutes. Remove from heat and stir 1/3 cup sugar into rhubarb mixture; set aside to cool to room temperature, about 30 minutes.
Whisk flour, baking powder, 1 teaspoon sugar, and salt together in a large bowl. Whisk milk, melted butter, egg, and vanilla together in a cup; stir milk mixture into flour mixture to form a smooth batter. Stir 1 cup of the cooled rhubarb mixture into batter.
Heat a lightly oiled griddle over medium-high heat. Drop batter by 1/3 cupfuls onto griddle; cook until bubbles form and edges are dry, 3 to 4 minutes. Flip pancakes; cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.