Police are appealing for witnesses after one of the listed ornate gates to the Quakers Walk footpath in Devizes were damaged between 4pm yesterday and 8am today.
A dog walker called the police this morning, worried that the gates were in a dangerous condition after being hit by a vehicle.
PC Cathy Byers said: "The gates are, in fact, structurally safe but they have clearly been damaged.
"There were shards of yellow plastic there, with blue paint on, which could have come from a trailer - I don't think they are from a vehicle bumper.
"We would like anyone who was in the area and saw anything which could be helpful to call 101 quoting incident log 68 of 22/08/14."
The Quakers Walk gates were restored last year, complete with dolphin emblems which had been absent from the roundels in the gates for more than 40 years.
Wiltshire Council took the opportunity to have new dolphins made when the gates were being restored.
The dolphins were the symbol of the Colston family crest. The Colstons owned Roundway Park and the Quakers Walk gatehouse. The gates are Grade II listed.