"Protecting this world-class landscape would not only preserve an area of unparalleled scenic beauty and rich cultural heritage," the letter said, "it would also foster a healthy America."
The Greater Canyonlands Coalition, a collection of environmental groups, is inviting other health professionals from around the country to add their names to an online letter.
Travis Mickelson, a child psychiatrist in Salt Lake City, said arguments over wild lands are typically about natural resources or economics.
"We don't appreciate how important our physical, mental and emotional health is," he said.
Wild areas "are potential, powerful healing tools," Mickelson said. "If we can protect them in this generation … then two or three generations from now, we'll still have them."
Michael Cumming, a veteran of the Iraq war and graduate student at the University of Utah, said he signed the letter because of the importance of such wild places to veterans' recovery.
Climbing with fellow veterans helped him deal with post-traumatic stress disorder, and now Cumming has created a nonprofit, dubbed Operation Climb On, to take other veterans climbing.
Veterans, he said, "have given so much for the country. To protect beautiful areas such as Greater Canyonlands can do so much for them."
Outdoor retailers, naturalists and others have been pressing Obama to designate the Greater Canyonlands monument.