Add 4 cups water to a skillet and bring to a boil. Add ramen and cook until soft, about 5 minutes.
Meanwhile, melt butter in another skillet over medium heat. Add carrots, zucchini, and onion and saute until vegetables have softened, about 5 minutes. Add shredded chicken, teriyaki sauce, salt, and pepper and cook until heated through and sauce has thickened, 3 to 5 minutes.
Drain ramen and add to the vegetable and chicken mixture. Toss and add more teriyaki as needed.