Antonio Nararainsami, 36, and several relatives, including his two young daughters, were leaving the stadium at the end of Tuesday night's game against the Washington Nationals when he fell in a section below the left field stands and landed on a concrete floor.
Nararainsami, a Guyanese native who lived in Brooklyn, was taken to a hospital, where he was pronounced dead half an hour later.
Kevin Prashad, a cousin who attended the game, said Nararainsami was walking down the escalator, which wasn't moving, and was holding the hand rail when he "lost his footing."
But a police source told Newsday that there were some reports that the victim was "surfing down the railing ... Witnesses said he had jumped on the rubber railing ... and he was sliding down when he lost his balance."
The Mets said in a statement that they had been "advised of a tragic accident that resulted in the death of a fan." They said team officials and police were investigating.
"Our deepest and heartfelt condolences go out to the fan's family," the team's statement said.
The death of Nararainsami, who was wearing a Mets cap when he fell, appeared to be an accident, and no charges had been filed, police said.
Nararainsami installed heating and air conditioning systems for a living, loved sports and was the captain of a local cricket club, his relatives said. His wife, pregnant with their third child, had stayed home while he attended the game.
Nararainsami's death wasn't the first at Shea. In 1985, a 21-year-old Yonkers man fell 100 feet from an escalator and was killed.
This is the Mets' last season at Shea Stadium. A new stadium, Citi Field, is scheduled to open next year.
Tuesday's game, which the Mets won 6-0, had celebrated Jackie Robinson Day, the 61st anniversary of when the Brooklyn Dodgers legend broke major league baseball's color barrier.