Police and paramedics responded to the area of the Etz Jacob Congregation/ Ohel Chana High School in the 7600 block of Beverly Boulevard at 12:24 p.m.
The individual who was shot, Zhoie Perez, captured the encounter on cellphone video.
In the video, the security guard stood behind a gate as Perez approached while filming. The guard drew a firearm and pointed it low, but it appeared to go off in his hand. It's not clear from the video whether the shooting was intentional.
Perez can then be heard shouting: "(Expletive) shot me. (Expletive) shot me in the leg!"
Police questioned the security guard after the incident and said Thursday night he has been arrested on suspicion of assault with a deadly weapon.
He was identified as 44-year-old Edduin Zelayagrunfeld.
Eyewitness News spoke to Perez after the incident.
"I was just filming the exterior of the synagogue and getting a lot of the architecture and all that," Perez said.
The synagogue is also home to an all-girls Jewish high school. The principal there said Perez was filming the girls, which made the staff and students uncomfortable.
"As a school that educates minors - their safety and security is a top priority for us. We have called 911 and the threats hotline multiple times," Yehudis Farkash said.
A witness to the shooting said he agreed that Perez was antagonizing the security guard.
"They were just like at the doorway videotaping the synagogue and all the young girls that are coming in and going, coming in and leaving. It was just strange," he said.
After the shooting, she got down on the sidewalk and behind a car. She says the security guard came out and continued to confront her.
"He leaves the gate, comes out on the sidewalk with his gun drawn again and says 'Try to break in. That was a warning shot, I'll kill you for real next time,'" Perez recalled.
As a bystander tried to help Perez, the guard continued yelling and said he did not shoot Perez, but shot at the ground.
Perez was treated for her injury, but did not go to a hospital.
Farkash said she wishes Perez a speedy recovery.
Warning: Video contains explicit language