The vehicle was deliberately torched in Church Street in the early hours of Saturday morning.
Officers have appealed for members of the public to come forward and call 101.
The incident took place just days after fire crews were despatched to Bruart Avenue in Stenhousemuir on Monday, August 19 to attend to a three-car blaze.
A Scottish Fire and Rescue Service spokeswoman said: “Two appliances were used and the fires were extinguished by 3.11am.”
Police were also alerted to early morning car fires in the town’s Bruce Drive and Lamond View that same day.