Police said the youngster was pronounced dead at the Beamish museum in Stanley, County Durham, just before 3pm yesterday.
The engine driver was taken to hospital suffering from shock, said Inspector Steve Dowdle, of Durham Constabulary.
Police will now conduct a joint inquiry with the Health and Safety Executive into the death at the museum in Gateshead, which recreates urban life in the North East as it was in 1913, complete with trams, a working farm and school.
Insp Dowdle said: "The engine driver will be spoken to at an appropriate time."
Neither the driver nor the boy were visitors, he added.
Museum director Richard Evans said: "We are naturally shocked and our thoughts are with the boy's family. We took an immediate decision to shut the museum for the day.
"The identities of those involved are not being released, but it is understood that neither of them were visitors to the museum.
"Detectives and roads policing officers are at the scene to establish exactly what took place and the Health and Safety Executive is also at the scene.
"We took an immediate decision to close the museum for the rest of the day as we support the joint investigation."
The Beamish Museum's attractions include mid-19th-century drift mine, which was reopened as a tourist attraction in 1970. A number of period films and television dramas have used the historic backdrop for their productions.
It describes itself as the "living museum of the north" and claims the tell the story of life for people in the north-east during the Georgian, Victorian, and Edwardian periods.