"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 club also said in a statement that it will work with the San Francisco Police Department to "step up enforcement in and around the ballpark [Thursday] and throughout the rest of this final homestand."
"It is sad. It's a shame that we're seeing this at sporting events," said Giants manager Bruce Bochy. "It breaks your heart that a young man lost his life. I don't get it."
The Dodgers also released a statement on Denver's tragic death:
"The Dodgers are shocked and saddened to learn of the death of Jonathan Denver, who is the son of one of our security guards.
"There is no rational explanation for this senseless act which resulted in Jonathan's death. The pain that this has caused his family and friends is unimaginable. Words are not enough to describe our sadness. Our thoughts and prayers are with him and his family during this extremely difficult time."
"It's disappointing," said Dodgers manager Don Mattingly. "It happens everywhere these days. Senseless. You see it all over the world, killing for no reason. ... I don't understand why."
Denver worked as a plumber's apprentice in Fort Bragg, Calif. According to the San Francisco Chronicle, he was stabbed near Third and Harrison streets (approximately a half-mile from the ballpark) around 11:30 p.m. PT Wednesday, less than 90 minutes after the game ended. Two men, ages 21 and 18, were arrested, according to the Chronicle, while 10 people -- both Dodgers and Giants fans -- were involved in the fight, one armed with a knife and another with a bat.
Denver died at San Francisco General Hospital. Another man was treated at the hospital after being punched numerous times, and he was later released, according to the newspaper report.
Adam Berry is a reporter for MLB.com. Follow him on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.