Firefighters were called to put out the disused static caravan at Park Road in Norton at 3.44pm.
They said the whole structure suffered severe fire, heat and smoke damage, and believe it was started by youths with matches.
Earlier in the afternoon - at 3.10pm - crews from Malton and Scarborough were called to put out a metal clad garage which was alight at Main Road, Helperthorpe, near Malton.
Firefighters said sparks from an angle grinder had caused the flames.
Several vehicles had been removed from the garage by the time firefighters arrived and were not damaged.