The victim, a woman, was struck by a car at around 11.30pm on Sunday on Derrington Lane, a turning off the A518 Newport Road.
The woman, believed to be from Stafford, was pronounced dead at the scene on the road near to the village of Derrington in Stafford.
Ambulance crews and police attended but nothing could be done to save her. Officers believe she had been walking along the road when she was struck.
A 56-year-old man from Telford was arrested on Monday afternoon on suspicion of causing death by dangerous driving and is in custody.
Detective Inspector Pete Goodwin, from Staffordshire Police, said the investigation was ongoing and urged anyone with information to come forward.
Det Insp Goodwin said: "The information the public has been able to provide has been very helpful, so thank you to everyone who has been in touch.
"Our enquiries are continuing and we are still keen to hear from anyone who may have witnessed the incident or may have useful CCTV or dashcam footage."
The road was temporarily closed in the aftermath of the incident but reopened on Monday morning as investigations into the woman's death continued.
Councillor Raymond Sutherland, who represents the area on Stafford Borough Council, said the news was “very very sad” – but said the road was not a notorious stretch although was very dark at night with no lights on it.
Anyone with CCTV or dash-cam footage or information about the incident is urged to contact Staffordshire Police via social media or on 101, reference 775 of August 29.