The blaze happened in Massey Crescent, Harlescott, at around 3.40am. Nobody was hurt in the incident.
Police have been contacted by the Shropshire Star to confirm whether or not they are investigating it as arson.
A Shropshire Fire and Rescue Service spokesman said: "At 3.41am we received a call reporting a fire classified as car fire in Shrewsbury.
"One car fully involved in fire. Crews extinguished using two hose reel jets and two breathing apparatus.
"One fire appliance was mobilised from Shrewsbury. A fire investigation officer was in attendance."