Malmesbury Police have appealed for witnesses to the incident, which took place at around 4.30pm just off the Fosse Way at Easton Grey.
They were called out to reports of lots of people and vehicles congregating close to Whatley Manor.
In a statement, police said: “Whilst officers were dispersing the crowd, one of our police vehicles was deliberately damaged.
“We believe that this was witnessed by a couple of people but officers were unable to take his details due to the dynamic situation.”
The witnesses were described by police as a white male, possibly with a French accent, walking two dogs, and a female with blonde hair, both possibly in their 40s.
If this was you, or if you have any further information regarding this incident, please call 101 and quote log number 203.