Vernon is an unincorporated community and census-designated place in Apache County, Arizona, United States. As of the 2010 census it had a population of 122. Vernon is 19 miles east of Show Low. Vernon has a post office with ZIP code 85940.Vernon was settled by B.H. Wilhelm Jr, who named it in 1894 for W.T. Vernon. It was important at first as a sawmill town, but as activity diminished, people moved away. It had been a Mormon ward, but they disbanded it in 1954, when the sawmill business finally moved to the vicinity of Lakeside.