The shooting happened Wednesday evening in a parking lot at a campus shared by Sem Yeto and Fairfield High School.
Authorities said roughly 1,000 people were attending the graduation ceremony at Schaefer Stadium when gunfire broke out around 7:15 p.m.
Baker was killed, and three others -- ages 11, 20 and 25 -- were also struck.
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Students who spoke with ABC7 Eyewitness News on Thursday said Baker had just graduated from Sem Yeto Continuation High School.
Police have not identified the other victims and said no arrests have been made.
"Detectives are working diligently to follow all available leads and are committed to bringing those responsible for this senseless act of violence to justice," Faifield police said in a statement.
The Fairfield-Suisun Unified School District said Friday night's Fairfield High School graduation were moved to another school "out of respect for the community." The district also emphasized that officials do not believe there is an ongoing threat.
Anyone with information is strongly encouraged to contact the Fairfield Police Department.