The collision took place on Maesbury Road near the town's industrial estate on Tuesday, January 11, at about 5.40pm.
It involved a Vauxhall Agila and a stationary lorry parked on the side of the road.
The driver of the Vauxhall was taken to the Royal Shrewsbury Hospital with serious injuries.
Police closed the road for several hours after the crash.
Officers are asking anyone who may have any information or dashcam footage of the incident to contact 101, quoting reference number 00146_I_05012022 or online at www.westmercia.police.uk/tua/tell-us-about
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org