They believe the red Kubota tractor which was fitted with a six foot grass cutter on the front was loaded onto a vehicle during a nightime raid.
They are now appealing for those involved in agricultrual or land-management work to keep a lookout for the stolen vehicle.
In particular, officers want to hear from anyone contacted by the thieves trying to sell it on.
Police Constable Ben Tanfield of Shrewsbury police said the thieves broke into a shed in the grounds of the cemetery in Longden Road between 4pm on July 6 and 8am the following day.
“They broke the padlock on a metal gate gaining entry to the cemetery maintenance yard.
“The thieves then forced open a locked roller shutter door to a shed garage from where they removed the tractor.”
The tractor, registration number DNO30JB, is owned by Shrewsbury and Atcham Borough Council. It appears to have been loaded onto a vehicle using two large wooden planks left at the scene.
The chasis number is 61420 and the engine number, 3A9172.
Anyone with information about the incident or with knowledge of the tractor‘s whereabouts, is asked to contact Pc Tanfield at Shrewsbury police station on 08457-444-888.