Three young men reportedly ran from the scene of the incident, which took place on Tuesday evening near Trench Lock,on the northbound A442 at around 5.50pm.
One of the drivers was taken to Royal Shrewsbury Hospital with non-life changing injuries.
Fire crews from Telford Central and Wellington attended as well as the ambulance service and police.
A spokesman for police teams in Telford and Wrekin said: "Three young men, who were travelling in a grey VW Passat that was involved in the collision, ran away from the scene.
"Officers would like to hear from anyone who witnessed, or captured on dash cam, the incident or the young men leaving the scene.
"Anyone with any information is asked to please visit orlo.uk/JtAgO quoting incident 463 of June 21."