Lt. Charles Hampton of the Atlanta Police Department homicide unit confirmed the death hours after the fall in the seventh inning.
A man identified by CNN as George Murrey, 60, of Alpharetta, Georgia, died upon arrival at Grady Memorial Hospital after falling at least 40 feet from the top deck to the concrete on the first level.
Fans told ESPN that he fell as he was yelling toward the field as the Yankees’ slugger Alex Rodriguez came up to bat — to lusty boos — in the top of the seventh inning.
The game wasn't delayed while medical personnel treated the man for about 10 minutes, applying CPR before putting him on a backboard.
Hampton said police don't suspect foul play at this point. He said no fans were hurt in the 200-level seats where Murrey fell from section 401, landing close to an area where players' wives and families sit.
There was blood on the concrete surface around the seats.
Murrey's death is the third death from a fall at Turner Field in eight seasons. In 2013, a fan's death was ruled a suicide; in 2008, police cited alcohol as a factor after a man died.
Yankees shortstop Didi Gregorius was standing on second base, following his double, when he saw the man fall.
"I was thinking about it the whole time," Gregorius said after the Yankees won 3-1. "All I can say is my condolences to the family. It was right in front of the camera in the press box. He hit the wires."
A sellout crowd of 49,243 was the largest of the season at Turner Field. The Braves are set to move into a new suburban stadium in 2017.