The police said the 4-year-old was from Lehi. A statement from the hospital identified the boy as Carson Dean Cheney.
"This tragic accident has taken the life of our energetic, sweet, beloved little boy, Carson Dean Cheney. We appreciate your thoughts and prayers, but wish for privacy at this difficult time," the boy's grandmother, Geri Gibbs, said in the statement from the hospital.
The police said the 4-year-old was from Lehi. The police did not immediately make public his name.
The Police Department and the Park City Fire District were called to the cemetery at a little after 6 p.m. He was taken to the Park City Medical Center in an ambulance. He died at the hospital, the police said.
Phil Kirk, a police captain, said the headstone is large. The boy's family called 911. The family freed the boy from underneath the headstone, Kirk said. He was not sure whether the headstone marked the grave of a family member.
"Everybody was doing their best to try to save this young boy's life. We're all struggling with this one," Kirk said.
The police said the death was an accident.
Bruce Erickson, the president of the Glenwood Cemetery Association, declined to provide details about the headstone. He said the association, which owns the land where the cemetery is located and maintains the grounds, closed the cemetery at approximately 7 p.m. on Thursday. The cemetery is expected to reopen as early as Monday.
Erickson said the decision to close the cemetery was out of respect for the loss of the boy and out of respect for the family of the person buried underneath the headstone. He said the decision also was to respect the other graves.
There are approximately 900 graves in Glenwood Cemetery, which is located off Silver King Drive in Thaynes Canyon. The cemetery dates to 1885.