According to the report, the fight happened after the Giants were beaten 6-1 by Oakland on Thursday.
According to San Francisco police, the woman, who was wearing an A's cap, was punched in the face trying to break up a fight between two men and hit her head on the sidewalk.
More from CBS San Francisco:
She was unresponsive when an ambulance took her to the hospital, and her condition was unknown. Witnesses told police that two suspects, both men, drove away in a gold colored Toyota Tundra truck.
This is latest incident outside a ballpark involving fans fighting.
In September, a Dodgers fan was stabbed to death near AT&T Park after a Giants-Dodgers game, but no charges were filed in that case after prosecutors said they could not prove their case beyond a reasonable doubt.
- Scooby Axson