The crash happened on the A49 in Woofferton near Ludlow at about 7.30pm on Friday, October 30.
It involved a blue Vauxhall Corsa and grey Skoda Fabia.
The driver of the Skoda, an elderly woman, suffered serious injuries and is in critical condition in hospital.
West Mercia Police is appealing for witnesses.
Anybody with information can contact the police on 101.
Alternatively, contact Crimestoppers anonymously on 0800555111 or crimestoppers-uk.org