The blaze started in the van, which was parked in Union Street. It then spread to a nearby house.
A spokesman for Shropshire Fire & Rescue said: "The van was well alight when the crew arrived. The fire caused some damage to the nearby property.
"Fortunately no-one was injured and no-one had to be evacuated from the property, although the ambulance attended as a precaution.
"We don't know the cause of the fire yet, but it is being investigated by police."
Firefighters had to wear breathing apparatus as they tackled the blaze.
The blaze broke out shortly before 3pm on Friday, and firefighters used a hose reel jet to tackle the fire, the spokesman added.
Anyone with information about the cause of the fire is asked to contact police on 101.