Police were conducting a search of the hospital grounds when the body was found in a vehicle parked on site shortly after 1.30pm on Friday.
A 46-year-old woman had been reported as missing on Thursday.
West Midlands Police spokesman Pete Edney said the death is not being treated as suspicious and has been referred to the coroner.
The matter has been reported to the force's Professional Standards Department and the Independent Police Complaints Commission as a matter of course in these circumstances.
Dudley Group NHS Foundation Trust runs Russells Hall Hospital.
Trust chief executive Paula Clark said: "We can confirm there has been an incident in the main visitor car park at Russells Hall Hospital.
"The incident is being managed by West Midlands Police."