Authorities were called to the school at 7:05 am, and officials said that the male suspect was apprehended at a nearby Vons grocery store after the shooting.
McDonnell said the 14-year-old suspect had fired multiple gunshots in a courtyard but did not elaborate on whether the teen was aiming for anyone in particular.
The department added that the suspect was arrested off-campus and a rifle was recovered off-campus, and the shooting appears to be an isolated incident with no further threats to the community. A 12-year-old girl was booked for negligent discharge of a firearm in that shooting, which was considered "unintentional", Los Angeles police said.
"All of the Palmdale Elementary Schools were put on lockdown".
Investigators were trying to determine what led up to the shooting and whether the boys knew each other.
At least one person was injured as of 7:30 a.m. and drove themselves to the hospital, according to officials.
The Los Angeles County Sheriff's Department said one victim was shot in the arm and is in stable condition.
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He says one student was shot in the arm and the shooting stemmed from a dispute between the shooter and the victim.
The lockdown at the school was lifted several hours after the shooting and school officials said they would begin reuniting students with their parents.
The Los Angeles County sheriff's department said on Twitter Friday morning that the school has been searched and cleared.
Witnesses who were outside the school described hearing a gunshot or gunshots, and seeing students running from the building.
Palmdale is about 40 miles north of Los Angeles.
Firefighter-paramedics told NBC Los Angeles they received a report of one person with a gunshot wound, though any injuries couldn't be independently confirmed. More information will be provided as it becomes available.
Betsy Sanchez, a spokeswoman for the Antelope Valley Union High School District, said the office is in contact with victim's family.