The woman was taken to hospital with what police described as serious injuries, while a second man was hurt in the three-car crash on the outskirts of Shrewsbury.
The collision involved a car driving on the wrong side of the A488 near Lea Cross at about 5pm yesterday.
West Mercia Police said a Volkswagen Polo being driven on the wrong side of the road caused a collision with two other vehicles – a Vauxhall Astra and Volkswagen Scirocco.
The driver of the Astra, a woman, suffered serious injuries and was taken to Royal Shrewsbury Hospital. The Scirocco driver, a man, suffered minor injuries to his hip but did not need hospital treatment.
The crash caused extensive damage to the vehicles involved and shut the road for some time.
The driver of the offending vehicle failed to stop at the incident and police are now asking for help tracking him down.
Pc Simon Brenton said: “We are appealing to the public to help us locate the offending driver whose disregard for other’s safety has left a woman seriously injured and another person hurt.
"They have also caused extensive damage to the vehicles involved and caused the road to be closed for some time.
“This type of dangerous driving will not be tolerated and we ask the community to help us find the offender whilst we continue our enquiries.”
West Midlands Ambulance Service, who took the woman to hospital, said she had got out of the vehicle herself and was treated for what were thought to be minor injuries.
Anyone with information or dash-cam footage is urged to call police on 101 quoting incident 00474i of September 24, 2020
Alternatively, contact Crimestoppers anonymously on 0800555111 or crimestoppers-uk.org