Police said the fire caused about £800 of damage to the speed camera on Station Road, Ketley.
It has now been taken down to be rehoused before it is put back up again.
The camera mounting box, frame and stand were all damaged, although there was no damage to the actual camera.
Chris Ammonds, a spokesman for West Mercia Police, said: "We believe that some time between 12.30am and 1.20am this morning, a person or a number of people attempted to set alight the roadside speed camera.
"There was scorching to the mounting box, the frame and stand of the camera on Station Road in Ketley.
"We received the call at 1.22am and we were requested to attend by the fire service. We are investigating the matter.
"It appears that the camera itself was not damaged, and it has been removed to be rehoused and will then be put back in place."
A spokeswoman for Shropshire Fire and Rescue said: "The fire was caused by a tyre which was set alight and wrapped around the base of the camera. We were called out to the fire at 1.15am this morning."
Witnesses should contact police on 101.