The unidentified man was discovered with head injuries suggesting a fall at around 5 a.m., San Francisco General Hospital spokeswoman Rachael Kagan said.
The man, who had no wallet or identification when he was found, remains unconscious in critical condition, and the authorities are trying to contact his relatives, she said.
He is a white male between 30 and 40 years old. He is around 5 feet 10 inches tall and weighs around 165 pounds. He has brown hair, brown eyes and no tattoos or distinguishing marks, Kagan said.
The victim was wearing Levis jeans, black leather shoes, and no shirt when he arrived at the trauma center, she said. He was carrying a Jeep key and a silver house key.
The hospital released photos of the man on Sunday afternoon in an effort to identify him.
Anyone with information is asked to contact the San Francisco Sheriff's Department at (415) 206-8063.