The footage, taken by a construction working who was passing by, shows the unidentified teacher trying to pull up his pants after the incident, which took place in the middle of Carthay Center Elementary School's playground.
Parents were alerted about the incident through both a robocall and a letter that was sent home with kids.
According to the notification, "an individual began behaving in an usual way, prompting us to contact law enforcement. As a precaution, our school went on a brief lockdown while officers responded and took the individual in custody."
The second- and fifth-grade students who witnessed the incident took shelter in nearby classrooms.
"He was supposed to be helping them learn PE, run around and have fun," one parent said.
"But he undressed and started chasing the kids while he was naked, and then the kids ducked and dodged, ran into some of the classrooms and got safe haven that way."
"All of the kids saw his private parts. Very embarrassing, very upset," another parent added.
Los Angeles Unified School District officials said that they are unable to comment on the incident. However, they verified that the teacher was a contracted employee by the school and was approved to be on the school's campus. Mental health counseling has been made available to the children involved as school police continue to investigate the case.