Paul Henderson, the park's chief of interpretation, said Wall Arch collapsed sometime late Monday or early Tuesday.
The arch is along Devils Garden Trail, one of the most popular in the park. For years, the arch has been a favorite stopping point for photographers.
Henderson said the arch was claimed by forces that will eventually destroy others in the park: gravity and erosion.
"They all let go after a while," he said Friday.
He said it's the first collapse of a major arch in the park since nearby Landscape Arch fell in 1991. No one has reported seeing it fall.
Like others in the park, Wall Arch was formed by entrada sandstone that was whittled down over time into its distinctive and photogenic formation.
The arch, first reported and named in 1948, was more than 33 feet tall and 71 feet across. It ranked 12th in size among the park's estimated 2,000 arches.
Rock has continued to fall from the remaining arms of the arch forcing the closure of a portion of the trail.
Officials from the National Park Service and the Utah Geological Survey visited the site Thursday, noting stress fractures in the remaining formation. The trail won't be opened until the debris is cleared away and it's safe for visitors, Henderson said.