At least three nearby schools - David G. Millen Intermediate, Cottonwood Elementary and Ocotillo Elementary - were on lockdown, employees there said.
The boy injured was also 14, and police stated that he was taken to the hospital after being shot in the arm.
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.
School District Superintendent Raul Maldonado confirmed in a statement that there had been an active shooter on campus.
Authorities went to the high school in the 39000 block of 25th Street West in Palmdale about 7 a.m.
"All authorities are telling us right now is that they are working on the situation", Luke said.
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"That student is going to be OK", he said.
The school sign reads, "bully-free zone", at Highland High School where a shooting occurred on May 11, 2018 in Palmdale, California.
The off-duty LAPD officer who apprehended the suspect at the Vons supermarket said he had received a call from his mother, who stated that he ran away from the home that morning after they "were having trouble with him, McDonnell said".
"I thought he was joking, and I'm like, 'Don't mess around, that's not amusing, '" Salazar said.
On Friday, a gunman entered Highland High School in Palmdale, California and shot a student.
Bureau of Alcohol, Tobacco, Firearms and Explosives officials also responded to the shooting, the agency tweeted.
About a half hour after the Highland calls, gunshots were reported at the Manzanita Elementary School, located about seven miles away from Highland High School. More information will be provided as it becomes available.