Combine the bread crumbs, Monterey Jack cheese, and ranch dressing mix in a large bowl; set aside. Pour the milk into another bowl, then dip the chicken breasts into the milk. Gently press the chicken into the bread crumb mixture. Arrange the chicken in a 9x13-inch baking dish.
Bake the chicken breasts in the preheated oven until no longer pink in the center and the juices run clear, 40 to 45 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).