The fire happened at Blists Hill Victorian Museum at around 7.44am. A 4x4 was 75 per cent destroyed.
Shropshire Fire and Rescue said fire was accidental. Nobody was hurt in the incident.
It tweeted: "At 07.44hrs 14.11.19 crews attended a vehicle on fire in Blists Hill, Ironbridge, Fire Investigation called out and confirmed the cause as accidental."
The museum was not affected by the fire.