Police say a student managed to fire the weapon, which was locked to the side of a motorcycle that was on display for Red Ribbon Week at Newman Elementary School on Wednesday.
According to Police Chief Miles Pruitt, department rules state the rifle chamber should be empty when it is mounted.
"The preliminary investigation has shown that the established safeguards and procedures were not followed," Pruitt said. "It is unfortunate that this event occurred and I will make every effort to ensure it does not happen again."
The weapons mount holding the rifle had several fail-safes, including a metal plate, police said.
"The bullet disintegrated when discharged by striking a metal plate where the barrel rests against the weapons mount," and fragments apparently struck some children and caused minor injuries, Chino police spokeswoman Tamrin Olden said.
Two students who were hurt were treated at a hospital and released. A third was examined at the school and released to parents, Olden said.
Rifles have been removed from other police motorcycles while the shooting is under investigation, Olden said.
It remained unclear Thursday if an officer was nearby when the gun went off.
The Associated Press contributed to this report.