The fan was identified by the Fulton County Medical Examiner's Office on Sunday morning as 60-year-old Gregory K. Murrey. A native of Alpharetta, Georgia, Murrey will undergo an autopsy later Sunday, according to the medical examiner's office.
Murrey was given emergency medical treatment at Turner Field and was taken away on a stretcher after falling. He was pronounced dead at Grady Memorial Hospital.
Lt. Charles Hampton of the Atlanta Police Department homicide unit said police don't suspect foul play at this point. He said no fans were hurt in the lower-level seats where the man fell.
In a statement Sunday, the Braves said they were "deeply saddened by the loss of Greg Murrey at last night's game. Greg was a valued and longtime season-ticket holder and an incredibly passionate Braves fan. This tragic loss is felt throughout Braves Country, and the thoughts and prayers of the entire Braves organization continue to go out to his family and friends."
The team also tweeted a picture of Murrey.
According to witnesses seated in Section 401 behind home plate, Murrey was screaming at Alex Rodriguez, who had been sent up as a pinch hitter by the Yankees, when he suddenly lost his balance and fell approximately 50 feet to the concrete below, striking a railing on the way down.
There was blood left on the surface around the seats after Murrey was put on a backboard. A group of stadium medical personnel treated him for about 10 minutes, performing CPR. As the medical workers worked in a circle around Murrey, security officers cleared the area. The game continued as medical personnel attended to Murrey.
A witness said Braves representatives came around in the eighth inning to check on fans and offered them seats in suites, away from where Murrey fell.
A witness who asked not to be identified said she was seated a row in front of Murrey when he began shouting at Rodriguez.
"All of a sudden, he just flew right over the rail,'' she said. "I can't even function right now.''
Turner Field security refused to allow media access to the site of the accident.
"Huge condolences go out to that family," Braves pitcher Matt Wisler said. "You never want to hear something like that. We were all in the dugout paying more attention to that than the game when it first happened. That's terribly sad to hear. We really hope for the best for that family. That's sad to see something tragic like that happen at a game."
Gregorius said it was difficult to concentrate on the game after seeing the incident.
"I was thinking about it the whole time,'' he said. "All I can say is my condolences to the family.''
There was a large contingent of Yankees family members sitting in Section 202, right next to the aisle in which Murrey fell. A Yankees security officer estimated 45 to 50 family members were seated in the section, but none were injured.
McCann, the former Braves catcher who lives in Atlanta, had his wife, mother and children in the section, although his wife and children had left the stadium before the incident.
"My mom was right in the mix," he said. "All our families are up there, so you're just praying for the best. They were close. They were real close. Our hearts go out to the family. It's sickening.''
Some players' family members were escorted to a room near the Braves' clubhouse. Many, including Atlanta outfielder Cameron Maybin's son, were crying.
Yankees closer Andrew Miller caught a glimpse of the incident from the bullpen.
"I mean, most of us saw the net shaking, 'cause we were all watching Alex come up,'' he said. "I know it was kind of close to where a lot of tickets are left for our families and stuff, so guys were kinda freaked out about that. ... Terrible situation. I don't know what else to say.''
A security guard at the holding room for family members said witnesses saw Murrey trying to hang onto a wire that runs from the protective net behind the plate to under the press box.
He then fell the rest of the way into the seats. The force of his weight caused the wires and the mesh netting to shake for several seconds.
Yankees manager Joe Girardi said he was made aware of the incident from third-base umpire Dana DeMuth and Yankees third-base coach Joe Espada, who made a hand gesture toward the dugout indicating someone falling.
"I just remember I'm thinking, what does that mean? I didn't understand at first,'' Girardi said. "That's really sad, that something like that could happen at a ballpark.''
Major League Baseball said it had been in contact with the Braves and was monitoring the situation.
The announced crowd of 49,243 was the largest of the season at Turner Field.
This wasn't the first fan fatality at Turner Field. In August 2013, Ronald Lee Homer Jr., who was 30, fell 85 feet from a walkway on the fourth level of the stadium. Investigators from the Fulton County Medical Examiner's office later ruled that the death was a suicide. Police said Homer, of Conyers, Georgia, landed in the players' parking lot.
In 2008, Justin Hayes, who was 25, fell down a Turner Field stairwell during a game against the Mets. He died of head injuries, and police cited alcohol as a factor.
The Associated Press contributed to this report.