Bring chicken broth to a boil in a medium-sized saucepan then add rice and cover with a lid. Turn heat down to medium-low then simmer until rice is al dente, 13-15 minutes.
Turn off heat then stir in shredded zucchini, parmesan cheese, and butter then place a lid back on top and let sit for 5 minutes on the burner with the heat off. Taste then add salt if necessary, and then serve.