Alexander, who is also a reserve police officer, was reportedly making sure the gun wasn't loaded by pointing it at the ceiling as part of a firearms safety demonstration at Seaside High School.
Teachers are not permitted to possess firearms in California schools.
He emphasizes that it was not a bullet, and was "not life threatening".
The student was rushed to the hospital after school when his parents noticed blood on his shirt.
Ferrante said Alexander - who also is a Seaside City Council member - has been a reserve officer for the past 11 years, and described his track record as "positive and professional".
UPDATE 6:45pm: Diffenbaugh, in a follow up conversation, says it's against state law and district board policy to have a non-authorized individual carry a firearm on campus, and that Alexander was not authorized by the school district to have one.
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School resumed shortly after the incident once police and staff determined it was safe, said Marci McFadden, chief of communication and engagement with the Monterey Peninsula Unified School District.
Teachers can not legally possess firearms in California classrooms. Sand City Police Chief Brian Ferrante said that Alexander had his last gun safety training less than a year ago, and doesn't know why he would bring a loaded gun into a classroom.
A picture obtained by KSBW showed the student with small red bruising to his neck, which Gonzales said appeared to be caused by a bullet fragment. He was named reserve officer of the year in 2013.
Fermin Gonzalez is upset he was not informed about the incident by the school.
Earlier this month, a teacher from Dalton, Georgia was arrested after he fired at least one shot in his classroom. Because using anything besides a gun wouldn't have been as effective I guess and the best way to unload a gun is to shoot it in a class full of kids.
The incident comes amid a national debate on how to protect students from mass shootings like the one that took the lives of 17 students in Parkland, Fla., on February 14. "You take what is called a dummy gun, which looks like a real gun but you can't even put a magazine in it and you certainly can't put bullets in it".