Officer Gordon Shyy says the death came just after kickoff at about 1:30 p.m. in the 49ers' 34-28 win over Green Bay.
The victim, 32-year-old Hayward resident Kevin Hayes, was walking with his brother on the Jamestown pedestrian walkway when he fell and suffered serious injuries.
Off-duty medics and police officers gave him first aid until an ambulance arrived, but the man was declared dead from his injuries.
Multiple witnesses told police that the man appeared to be intoxicated at the time of his fall.
In a statement, 49ers spokesman Bob Lange confirmed the team had learned of the accident outside the stadium.
"We would like to express our deepest condolences to the family during this difficult time," he said in an email.
It was not clear how far Hayes fell from the Jamestown walkway, which goes around the outside of Candlestick.
The historic sports complex closes after this season and will be replaced by a shopping center. Next year, the 49ers will move into a $1.2 billion stadium at the team's Silicon Valley headquarters in Santa Clara.
Since 2003, there have been more than two dozen cases of fans falling at stadiums across the United States, according to the Institute for the Study of Sports Incidents.
Most recently in Atlanta, baseball fan Ronald Lee Homer Jr. died last month after falling 85 feet following a tumble over Turner Field's fourth-level railing. Homer's death was the third at an Atlanta stadium in the past year.
Also last month in Denver, Broncos fan Noel Robinson was injured when he fell about 10 feet from an escalator at a preseason game.
(The Associated Press contributed to this story)