The collision happened in Berwick Road, at around 6.50pm on Thursday.
The man had freed himself from the vehicle before firefighters arrived.
A Shropshire Fire & Rescue spokesman said: "At 6.50pm we received a call reporting that a road traffic collision had taken place in Shrewsbury.
"One fire appliance was mobilised from Shrewsbury.
"One casualty was being attended to by ambulance service."