Flames broke out overnight at Temple Israel of Hollywood at 7300 Hollywood Blvd. near Martel Avenue. The fire was quickly extinguished, causing minor damage.
Police said the suspect broke into a second-story classroom through a window, vandalized the room and started a small fire.
"Nobody was in when the break in occurred," Los Angeles Fire Capt. Jaime Moore said. "We believe that the break in took place overnight. However, when staff first arrived on scene is when they saw this individual exiting the building."
A surveillance camera at the synagogue caught an image of the suspect, who is believed to be a transient in his late 20s standing about 5-feet-11.
Along with the Los Angeles police and fire departments, the FBI and ATF were investigating the incident as part of a task force that looks into attacks on houses of worship.
People inside the temple were briefly evacuated to the parking lot as authorities investigated the scene.
"They asked us if we had seen anyone in a ski mask, but none of the valet workers had seen him," said Daniel Orozco, who works valet nearby.
Investigators declined to say what was collected and put in brown paper bags, only saying it was evidence.
Jacob Shneiderman, a student, and his mother, Jennifer, said it was upsetting to think about.
"We were thinking that we might die or that the school might burn down," the boy said.
Councilman Tom LaBonge is calling what happen at the temple a hate crime.
"Any time an institution is attacked it's hate crime, whether a church, temple or mosque," he said.
This is the second incident at a local Jewish house of worship in a week.
Anyone with information on the suspect is asked to call the fire department's arson investigators at (213) 485-6095.