The tragedy took place at around 11.45am on Monday, July 13 at Felbrigg Hall, near Cromer.
The man in his 70s died at the scene, despite the efforts of paramedics.
Following the death, the National Trust announced that the site was closed.
On the halls National Trust site, it reads “Felbrigg Hall, Garden and Estate is currently closed and will remain so on Tuesday 14 July.”
A spokesman for Norfolk Constabulary said the man’s next of kin had been informed.
He added: “Officers are investigating alongside colleagues from the Health and Safety Executive.”
A spokeswoman for the National Trust said, “Emergency services were called to the parkland at Felbrigg Hall on Monday 13th July after a member of the public was seriously injured while walking.
“Despite the efforts of the paramedics, the person tragically died at the scene.
“We are shocked and deeply saddened by this news, and our thoughts and condolences are with their family and friends at this incredibly difficult time.
“As an investigation is under way, we are unable to comment further.”