Police summoned to the home for a welfare check found the bodies of three adults and five minors, the statement said.
"Each appeared to have sustained gunshot wounds. At this time, we do not believe there is a threat to the public or that there are any suspects at large," the statement said.
"This investigation is still active and more information will be provided at a later time."
Enoch, with a population of about 8,000, is in southwestern Utah, about 250 miles (400 km) south of Salt Lake City.
(Reporting by Daniel Trotta; Editing by Tom Hogue)
