There were no World Cup games being screened at the time of the shooting, with the only match of the day in the tournament finishing around 2 p.m. local time (2100 GMT).
“One victim was pronounced deceased on scene. The second victim was transported to a local hospital with life-threatening injuries,” San Jose police said in a post on social media platform X.
“This incident is being investigated as a homicide. Several surrounding streets are closed in the area.”
The incident occurred at San Pedro Square, one of several places in the San Francisco Bay Area where huge crowds have gathered for lively “watch parties” showing World Cup matches on big screens.
The Bay Area has hosted five World Cup matches so far, with the last game a knockout match on Wednesday between Bosnia and co-hosts the United States.
A Reuters journalist at the scene saw a heavy police presence, multiple police vehicles and a person on a stretcher partially covered by a white sheet being rushed away from the area by people in uniforms.
The scene was cordoned off and most bars in the area were closed after the incident.
A security guard, who declined to be named because she was not authorized to speak to media, said she saw the injured person in distress.
“The person was still moaning and groaning. There was blood around his neck and upper back,” she said. “Police were talking to security and a couple of witnesses.”
There are several dozen fan zones across the Bay Area.