Durham Constabulary said the youngster was pronounced dead at the scene of the tragedy at the Beamish Museum, which was evacuated.
A police spokeswoman said the driver of the engine had been taken to hospital suffering from shock after the incident, which happened shortly before 3pm.
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Hide AdDurham Constabulary said officers were alerted by the ambulance service and were conducting a joint inquiry with the Health and Safety Executive.
Insp Steve Dowdle said: “The engine driver will be spoken to by police at an appropriate time and is being treated as a witness.
“The identities of those involved are not being released, but it is understood that neither of them were visitors to the museum.”
The museum’s director, Richard Evans, issued a statement through police.
“We are naturally shocked and our thoughts are with the boy’s family at this time,” he said.