Red Rock is an unincorporated community and census-designated place in Apache County, Arizona, United States. Red Rock is located on the Navajo Nation near the New Mexico border, 16 miles northeast of Lukachukai. Red Rock has a post office with ZIP code 86544; the post office uses the Red Valley name. As of the 2010 census, the Red Ro…Red Rock is an unincorporated community and census-designated place in Apache County, Arizona, United States. Red Rock is located on the Navajo Nation near the New Mexico border, 16 miles northeast of Lukachukai. Red Rock has a post office with ZIP code 86544; the post office uses the Red Valley name. As of the 2010 census, the Red Rock CDP had a population of 169.