Suhr said two suspects have been taken into custody, but another two remain at large. He did not release the suspects' identities.
Denver attended the game, which the Giants won 6-4, with relatives before they all left in the eighth inning and went to a bar. The suspects went to a nightclub in the area, but did not attend the game, Suhr said.
The two groups crossed paths on a street near the ballpark around 11:30 p.m.
The Giants and Dodgers are longtime division rivals. The Giants were the defending World Series champions. But this year, the Dodgers won the division while the Giants were set to miss the playoffs.
The Giants said in a statement that they were saddened to learn about the Denver's death.
"While details are still emerging, we want to be clear that there is absolutely no place in our community for this type of senseless violence," the team said in a statement.
The violence comes just three days after a teenage football fan was attacked at San Francisco's Candlestick Park during the San Francisco 49ers 27-7 loss to the Indianapolis Colts. Other violence broke out at the game on Sunday despite an increase in security. The stadium was also the site of two shootings, beatings and fights during a preseason game two years ago.
Stadium security and fan behavior also came under scrutiny when another Dodgers-Giants matchup saw a Northern California paramedic severely beaten. Bryan Stow, a Giants fan, suffered a traumatic brain injury after a beating by two men dressed in Dodgers gear following the March 31, 2011, home opener between the two longtime rivals.
The Giants are holding a fundraiser for Stow. The team will donate $10 from each ticket sold in certain sections of AT&T Park at Tuesday, Thursday and Sunday's games to a fund setup for Stow, Slaughter said.