Cleaners attended the toilets, on Oxford Street, on Friday and were met with heavy smoke.
The fire had started in a bin.
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."
The opening hours of the toilets had only recently been extended, to help bus drivers at the start and end of their shifts.
"This kind of criminality has to stop," added Cllr Grant.
The town council is also in the process of improving CCTV coverage and lighting in the surrounding area.
If anyone has any information, please contact Wiltshire Police on 101.
Wiltshire Police have been contacted for comment.