Police were contacted at around 4.45am and were notified of what was initially reported to be a serious collision involving a pedestrian on the A379, Embankment Road, at New Bridge, Kingsbridge.
Emergency services attended the incident.
The pedestrian, a 22-year-old woman, was seriously injured.
Despite the efforts of paramedics, she was pronounced deceased at the scene.
Her next of kin have been informed.
A road closure was put in place while officers from the Roads Policing Team carried out an examination of the scene. The road remains closed at this time.
DCI Ilona Rosson said: “Officers have arrested a man in his 30s from the Kingsbridge area on suspicion of murder. He remains in police custody and awaits questioning.”
The closure of the A379 remains in place at this time and we would like to thank the public for their continued patience whilst this investigation is ongoing.
“Enquiries continue into the circumstances surrounding this death and it is vital that any witnesses who were in the area around the time of the incident contact us immediately.
“We would also like to hear from any road users who may have captured footage via their dashcam, and anyone who believes they may have information that can assist investigating officers.”
If you witnessed the incident or have any information or dashcam footage that could help with enquiries, please contact Devon and Cornwall Police via their website or by calling 101 quoting reference number 50250099726.
Alternatively, independent charity Crimestoppers can be contacted anonymously online at its website or by calling freephone 0800 555111.