It happened around 7:29 p.m. in the 44600 block of Sierra Highway.
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According to deputies with the Lancaster Sheriff's Station, the suspect who was driving cut off a mother and father who were traveling in the area of Sierra Highway and East Avenue J.
The suspect then began following them through several surface streets, investigators said.
"While being pursued by the suspects, the victim driver slowed his vehicle, at which time the suspect driver pulled up along the passenger side of the victim's car and began shooting," read a statement released by the sheriff's department.
The 4-year-old boy, who was in the backseat, was struck by gunfire in the upper torso, investigators said. The parents rushed the boy to a local hospital where the child later died.
The suspect vehicle's was located in the area shortly after the shooting, according to the sheriff's department.
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A 29-year-old man and a 27-year-old woman have since been arrested in connection with the death.
Lancaster Mayor R. Rex Parris took to Facebook Saturday, saying the suspects were tracked by the city's recently installed flock camera safety net.
"We know where they've been, we know where they're going, so when a crime is committed, we can go back in time and find out where they are," he told ABC7.
No other injuries were reported.
As the investigation continues, Parris said he's heartbroken for the victims.
"We're praying for the family," he said. "We understand that this is a really good family. I've talked to members of their church. It's unimaginable that this could have been any of our families. It could have been any of us."
Anyone with information is urged to contact the Los Angeles County Sheriff's Department's Homicide Bureau at (323) 890-5500. You can also submit an anonymous tip by calling Crime Stoppers at (800) 222-TIPS (8477) or visiting the Crime Stoppers website.