Capt. Darren Harris said deputies believe the suspect was acting alone, but the investigation was continuing.
The Bureau of Alcohol, Tobacco and Firearms is also responding to the campus.
One student was shot in the arm following an argument between the two.
The man was seen at Highland High School in Palmdale in Southern California at 7.05am local time (12.05am Saturday AEST). However, Manzanita Elementary school had a scheduled day of active shooter training on Friday.
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The lockdown at the school was lifted several hours after the shooting and school officials said they would begin reuniting students with their parents.
So far, there is no evidence of a crime, according to LA County Sheriff's Deptartment. The school is located at 39055 25th Street West. Scanner traffic indicates that the gunman has been arrested at a Vons supermarket on 3027 Rancho Vista boulevard, about a mile north of the school.
The victim, whose age has not been released, was in stable condition, authorities tweeted.
A sheriff's spokesperson said it remained unconfirmed whether any shots were fired at the campus.
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The suspect has not been identified at this time, but is reported to be in police custody.
The incident was reported at about 7:00 a.m., the Sheriff's Department stated in a tweet. The footage was shot by Jon Baird of KNX1070 Newsradio, who told Storyful that deputies had confirmed the boy in the auto had been detained in connection with the shooting.
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