Three fans at the ballpark were "struck by fragments from what appears to be celebratory gunfire occurring throughout the city," police said Tuesday morning.
The shooting happened around 9:30 p.m., around the time that the post-game Independence Day fireworks display was lighting up the skies, police said.
A fourth victim also walked to a hospital to be treated.
One of the victims was an 11-year-old, the East Bay Times reported.
Oakland Police Chief LeRonne Armstrong said at a Tuesday afternoon press conference that a fifth person came forward to report that they were injured by a bullet fragment.
Armstrong said it does not appear that any guns were fired at the Coliseum, but in the area around the stadium.
"Our estimate is that it was in the radius around the Coliseum. So that could be in the residential areas around the Coliseum. It could be as far as our staff has estimated it could have been a mile away where those bullets could have been fired from," Armstrong said.
The police chief said based on bullet fragments investigators have recovered, it appears that a high-powered rifle was used in the incident.
All injuries were described as "non-life-threatening" by police.
Police said they are investigating the shooting.
A reward of up to $20,000 is available for information that leads to an arrest. Tips can be submitted to the Oakland police department's unit that investigates felony assaults at (510) 238-3426.