The 4x4 vehicle, which was parked outside Hope Street Mosque, suffered extensive damage in the fire.
West Yorkshire Police have confirmed they are treating the incident as arson.
A West Yorkshire Police spokeswoman said: "We were called at 6.06am this morning to reports of a car on fire at Hope Street in Dewsbury.
" Officers attended and are investigating the criminal damage as arson.
A spokesperson for West Yorkshire Fire and Rescue Service said: "We were called at 6.08am to a vehicle fire in Hope Street in Dewsbury.
"We sent one appliance from Dewsbury and spent around 40 minutes there.
"Police were notified."