Officers on patrol through the town centre in the early hours of Saturday morning discovered 50 wreaths had been thrown around in Regent Street, where the Cenotaph War Memorial is.
Swindon South Police posted on Facebook: “This was a mindless act of vandalism and shows complete disregard for those servicemen and women that have given the ultimate sacrifice in service of this country.
“Enquiries are ongoing and we urge that anyone who was in the area at the time that has any information that could assist the police to contact 101 and ask to speak to SPC 4448 Scott-Barrett regarding CRN 54190003682.”
Police say it happened at 4.38am.
Chief Constable Kier Pritchard tweeted: “This is a total disgrace.
“I laid our @wiltshirepolice wreath at this Cenotaph on Sun 11th Nov 2018 alongside many war veterans to show respect to those who paid the ultimate sacrifice to provide the freedoms we enjoy today.
“Name those involved and help us identify them.”