Bryan Stow is in critical condition at Los Angeles County-USC Medical Center, where a neurosurgeon said that Stow suffered a severe skull fracture and bad bruising to his frontal lobe.
Dr. Gabriel Zada said Stow is showing signs of "brain injury and dysfunction."
Stow's family spoke to the media outside the hospital Tuesday afternoon about his attack.
"During the game, my wife received a text from Bryan where he basically said he was scared inside the stadium," said Stow's cousin, John Stow.
Shortly after, the 41-year-old was knocked to the ground and hit his head on the pavement by two men wearing Dodgers clothing.
Doctors said they had to perform emergency surgery to save his life.
"His condition deteriorated and he required a life-saving operation to decompress the brain and reduce the pressures, which was successful," Zada said.
The Los Angeles Police Department released a composite sketch of the two suspects they say not only assaulted Stow, but may have assaulted others in the Dodger Stadium parking lot after the game.
"We believe there were approximately 100 people near where this assault took place, and we would like to reach out to them to contact us and provide any information they may have," said Los Angeles Police Det. Jose Carillo.
The Los Angeles City Council is offering a $50,000 reward in addition to a $10,000 reward from Los Angeles County for information leading to the suspects. The rewards in the case now total $100,000, including $25,000 from the Dodgers, a $10,000 reward offered by the Giants and $5,000 from Stow's employer, American Medical Response.
Stow is a paramedic from Santa Cruz. A Facebook page dedicated to him has thousands of entries from both Dodgers and Giants fans wishing him a speedy recovery.
The Giants announced that their first home game against the Dodgers on Monday, April 11 will be dedicated to Stow. The Giants will collect donations at the park to benefit a fund established to support Stow and his family. The team will make an initial contribution of $10,000 to The Bryan Stow Fund. Also, proceeds from a silent auction scheduled for that day will benefit the fund.
Additionally, on Friday during the Giants' first home game of the season, the team will pay tribute to Stow in a special ceremony before the contest.
Stow's family says the outpouring of support has been overwhelming.
"They weren't true Dodgers fans," said the victim's sister, Erin Collins. "Seeing all the support from the Dodgers fans, we really want to thank everybody."
Anyone with information is asked to call the LAPD at (877) 527-3247.
The Associated Press contributed to this report.