The attack occurred at around 4pm local time (9pm GMT) on Friday at New Hampshire Hospital in the city of Concord.
Governor Chris Sununu said the incident had been contained, adding: “While the scene remains active as the campus is cleared, the suspect is deceased.
“The state immediately mobilised, and first responders and law enforcement are on the scene. We will provide as many details as possible as this situation unfolds.”
New Hampshire Hospital is the state psychiatric hospital, located in the state’s capital.
Aerials photos of the hospital show an active scene with numerous police cars with lights flashing outside.
State police spokesman Colonel Mark Hall said the situation was “contained to the front lobby” of the hospital.
He added that one suspicious vehicle had been located near the scene.
“All patients are safe and we are asking people to avoid the area as investigation continues,” he said emphasising there was “no active shooter threat to the public”.
The New Hampshire Department of Homeland Security and Emergency Management said on X, formerly Twitter: “The situation at New Hampshire Hospital has been contained. The scene remains active. The suspect is deceased.
“We are aware of the situation unfolding at the New Hampshire Hospital. Police are on scene and responding.”
It is not known how many people have been hurt. The hospital is reportedly a psychiatric facility.
Concord police and deputies from the Merrimack County Sheriff’s Department, along with state police, were at the scene.
Authorities were setting up a media centre at a nearby sports field.
New Hampshire State Police added: “Troopers are currently investigating a shooting at New Hampshire State Hospital in Concord. There are multiple victims.”
Friday’s shooting was the latest act of violence at a US hospital.
Medical centres nationwide have struggled to adapt to the growing threats, which have helped make healthcare one of the nation’s most violent fields.