Fairfield police said the man had attempted to rob a teenage boy of his iPod and punched him in the face in the 1600 block of Union Avenue at about 4:45 p.m.
A 29-year-old woman and another bystander began yelling at the suspect, who fled - but as he was fleeing he turned toward the woman and opened fire, police said.
The woman was hit and was taken to a hospital.
Police searched the area but were unable to locate the suspect, who is described as a white male, 5 feet 10 inches tall, 180 pounds, with a buzz haircut. He was wearing black-and-red jeans, a white T-shirt and a black hoodie.
Police announced a $1,000 cash reward for information leading to an arrest.
Anyone with information on the shooting is asked to contact the Fairfield Police Department at (707) 428-7300, or Solano Crime Stoppers at (707) 644-STOP.
