Cleaners attended the toilets, on Oxford Street, on Friday (April 16) and were met with heavy smoke.
"This kind of criminality has to stop," councillor Gavin Grant said.
A spokeswoman from the fire service said: "We were called to the public toilets in Oxford Street, Malmesbury at 5.33pm on Friday, one crew from Chippenham attended and used a bucket of water to extinguish a small fire involving a plastic bin within the toilet block.
"The stop was at 6.34pm."
Posting on Facebook, Malmesbury councillor Gavin Grant said that extra police patrols in the area had been requested.
He wrote: "Yet again, criminals have attacked our Covid compliant loos, attempting to set fire to our disabled loo behind the Town Hall this afternoon. Thank you to the fire service and our two PCSOs for attempting promptly.
"At around 5pm our Town Hall cleaners arrived and opened the disabled loo door to find it engulfed in smoke. A fire had been set in the bin, air vents blocked and a serious attempt made to disable the release mechanism on the door."
A Wiltshire Police spokesman said: “At around 6pm last Friday (16/04) we were alerted by the fire service to a small fire at the public toilets near the Town Hall in Malmesbury.
“The fire is believed to have started at around 5pm and began in a bin inside the toilets.
“Thankfully nobody was injured.
“At this stage we believe the fire was started deliberately and are carrying out enquiries.
“Nobody has been arrested, but we would urge anyone with information to call us on 101, quoting crime reference 54210035558. Alternatively you can call Crimestoppers anonymously on 0800 555111.”
Cllr Grant told the Gazette: “This is another but much more serious attack on an important, new facilities in Malmesbury. This was an attack in brad day light. Arson is a very serious crime. Our cleaners or anyone else including a disabled child could easily have been seriously hurt when they opened the loo door where the fire had been set. This has to stop.
"We need people who know something or saw anything to tell the Police. As for the criminals who did this, they should know the Police will track them down and as a Town Council we will not hesitate to press charges.”
The opening hours of the toilets had only recently been extended, to help bus drivers at the start and end of their shifts.
The town council is also in the process of improving CCTV coverage and lighting in the surrounding area.