The 26-year-old died after being hit by a vehicle on the B4368 at Diddlebury, between Craven Arms and Much Wenlock, in the early hours of Saturday.
Police officers and the ambulance service attended the scene but were unable to save the victim.
Police have said the vehicle failed to stop and that "enquiries are ongoing" as they seek to find the person responsible.
Detective Inspector Dafydd Jones has appealed for people with information, who witnessed the incident, or who have dashcam footage to get in touch.
People can call police on 101 quoting incident 96i of April 30, or submit information through the force's website at westmercia.police.uk/tua/tell-us-about
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org