Early indications suggest 32-year-old Kevin Hayes of Hayward fell accidentally, San Francisco Police Chief Greg Suhr said.
"Alcohol may or may not have played a role to some varying degree, but right now, it looks like a very sad, tragic accident," Suhr said.
Hayes fell while walking with his brother on a bridge over four lanes of traffic outside the stadium, police said. Off-duty medics and police officers gave him first aid until an ambulance arrived, but authorities said he was declared dead from his injuries.
"We would like to express our deepest condolences to the family during this difficult time," 49ers spokesman Bob Lange said in an email.
The death came just after kickoff in what was eventually San Francisco's 34-28 win over Green Bay. Multiple witnesses reported that Hayes appeared to be intoxicated and having trouble walking before he fell over the rail to a sidewalk below.
"It certainly marred what otherwise a very happy day for fans who know this is the last opening game we will see in Candlestick," San Francisco Mayor Lee said.
Also Sunday, a railing collapsed at the Colts game against the Raiders in Indianapolis, injuring two unidentified fans who were leaning against the barrier above a tunnel leading to Oakland's locker room.
One person was taken away on a stretcher, while another left in a wheelchair, witnesses said.
After the Colts 21-17 victory, Barney Levengood, executive director of the Indiana Convention Center and Lucas Oil Stadium, issued a statement that said one of the people was released after receiving medical attention at the stadium. The other person was treated at the stadium and transported to Methodist Hospital for additional evaluation. Levengood said the second fan did not appear to be seriously injured.
Fan Dalton Tinklenberg of Kokomo., Ind., told The Indianapolis Star on Monday the railing that collapsed appeared to be wobbly. Stadium officials did not immediately return phone messages and emails from The Associated Press seeking comment.
Witnesses who saw the incident said the two fans were leaning against the railing and fell from the top of the tunnel onto the hard walkway used by Raiders players and coaches to reach the locker room.
Since 2003, there have been more than two dozen serious cases of fans falling at stadiums across the United States, according to the Institute for the Study of Sports Incidents.
That includes a 2007 fatality at Candlestick Park when a fan in the concession area misjudged a jump up to sit on a wall and fell instead from the upper concourse to the mezzanine level, said Alana Penza, director of the institute, which is part of the National Center for Spectator Sports Safety and Security, based at the University of Southern Mississippi.
"Sometimes a venue will say this was an accident, but other times they might decide to make adjustments," said Penza.
Historic Candlestick Park closes after this season and will be replaced by a shopping centre. Next year, the 49ers will move into a $1.2 billion stadium at the team's Silicon Valley headquarters in Santa Clara, a steeper design but with many built in safety rails.
Penza noted that stadium fatalities are not limited to football.
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.
AP National Writer Martha Mendoza in San Francisco and AP Sports Writer Michael Marot in Indianapolis contributed to this report.