Enoch was originally settled as part of an iron mission along with Cedar City and Parowan. The area was originally known as Johnson Springs, as named by Joel H. Johnson, the earliest known white settler. In 1890, the area's name was changed to Enoch, to avoid confusion with another settlement in Utah also named Johnson Springs. Enoch, along with nearby Grimshawville, Stevensville, and Williamsville, were officially incorporated on January 10, 1966
Enoch was incorporated on 10 January, 1966 and at that time absorbed the neighboring communities of Grimshawville, Stevensville and Williamsville.
There were 958 households out of which 59.0% had children under the age of 18 living with them, 79.6% were married couples living together, 7.8% had a female householder with no husband present, and 10.4% were non-families. 8.8% of all households were made up of individuals and 2.1% had someone living alone who was 65 years of age or older. The average household size was 3.62 and the average family size was 3.86.
In the city the population was spread out with 41.2% under the age of 18, 11.3% from 18 to 24, 28.2% from 25 to 44, 15.4% from 45 to 64, and 3.9% who were 65 years of age or older. The median age was 24 years. For every 100 females there were 97.2 males. For every 100 females age 18 and over, there were 95.4 males.
The median income for a household in the city was $37,368, and the median income for a family was $38,085. Males had a median income of $30,215 versus $19,688 for females. The per capita income for the city was $11,424. About 7.2% of families and 8.9% of the population were below the poverty line, including 12.1% of those under age 18 and 10.0% of those age 65 or over.