The fight around 10 p.m. Thursday involved a group of people and occurred a few blocks from the park. Officer Gordon Shyy says the group scattered when someone fired a shot.
Police did not find a gunshot victim at the scene and do not think anyone was struck by the bullet.
One person was taken to a hospital with a broken nose. It was not clear what sparked the fight or whether it had any connection to the game.
The Giants beat the St. Louis Cardinals to move on to the World Series.