The coroner has yet to establish the time or cause of Lynne Spalding's death.
The 57-year-old was admitted to the hospital for a bladder or urinary tract infection on Sept. 19. She vanished from her hospital room two days later.
Her body was found in a rarely used fourth-floor fire exit stairwell Tuesday during an unrelated inspection. The stairwell was several hundred feet from the unit where Spalding was being treated.
"What happened at our hospital is horrible," San Francisco General Hospital Chief Medical Officer Todd May said at a news conference Wednesday. "We are here to take care of patients, to heal them, to keep them safe. This has shaken us to our core. Our staff is devastated."
San Francisco Mayor Ed Lee has ordered officials from the state-run University of California, San Francisco Medical Center to review the hospital's security and patient safety procedures.
Spalding's family and friends spent days "scouring the streets of San Francisco with fliers because we were under the assumption that San Francisco General had been searched and Lynne was not there," the victim's friend and family spokesman David Perry said Wednesday.
Her family and friends are demanding answers from authorities and medical officials.
The Associated Press contributed to this report.