Los Angeles police said shortly after midnight, two men got into a physical confrontation that left the victim in critical but stable condition.
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No arrests were made and there was no information on a suspect, police said.
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.
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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.
Meantime, fans at Saturday's game against the Arizona Diamondbacks said they value the family atmosphere at the stadium and hope for no more violence.
"You bring your family here. Obviously, we have two little ones. You just don't want to bring any danger to them and stuff like that," said Dodger fan Kimberly Johnson. "You're here to enjoy the game, you know, not another sport after it."