Los Angeles police said two men got involved in an argument before one of them got punched once and fell to the ground. A witness immediately reported the incident to stadium personnel and the Los Angeles Police Department, authorities said.
The victim, a father of four, suffered a skull fracture and is on life support. His wife identified him as Rafael Reyna.
"He was hit and his head hit the ground and caused a skull fracture, and now his brain is swelling. He's bleeding on the brain," wife Christel Reyna said.
Christel Reyna said she was on the phone with her husband as he was leaving the stadium and in the parking lot. She then heard a woman and a man arguing with him.
"I was hearing the arguing happening and then I heard like a smack, a crack. It sounded like a baseball bat, and then I heard him start moaning," she said.
Christel Reyna's 22-year-old son and other family members have gathered at LAC+USC Medical Center. She hasn't yet told her younger children -- ranging in age from 11 to 15 -- about their father's condition.
"They're going to go in there and they're going to see him with tubes coming out of him. That's not the daddy they know," she said.
Dodger security and the LAPD are working together to identify the suspect. He may have driven off in a white SUV, possibly a Toyota 4Runner, police said. If you have any information about the incident, you're urged to call the LAPD.
Christel Reyna is also urging anyone who witnessed the altercation or knows the people involved to come forward.
"It hurts my heart," she cried. "This isn't supposed to happen. This isn't how you're supposed to live your life."
Friday night's game went into extra innings and ended with a loss. Fans who watched the game on television said they saw ugly encounters inside the stadium.
"I saw some people got a little excited, some people got angry. There's no need for that, it's supposed to be a family function, like we're all gathered together to celebrate a game," said fan Janelle Harrison.
Security was increased at Dodger Stadium after a series of violent incidents, including the beating of Giants fan Bryan Stow several years ago. Stow suffered severe brain damage.
Fans at Saturday's game against the Arizona Diamondbacks said they value the family atmosphere at the stadium and hope for no more violence.