The symbols were painted Saturday night outside Wilbur Elementary School on Crebs Avenue.
The Los Angeles Police Department says it has surveillance video from across the street that shows a lone man drawing the swastikas on a banner around 10:30 p.m. Saturday. The agency is not releasing that video.
"I was horrified by it," L.A. Mayor Karen Bass said.
She added that video shows the individual vandalizing the property.
A resident who recorded video of the swastikas attempted to cover up the symbols with spray paint.
School staff and members of the community later removed the entire banner so students wouldn't see it.
LAUSD Board Member Nick Melvoin released a statement over the weekend, saying the symbols were quickly removed. The district's first day of school was Thursday.
"I'm grateful for the prompt action and want to reiterate that no form of hate, including anti-Jewish hate, is tolerated in our schools," the statement read.
Police are investigating the incident as both vandalism and a hate crime. Anyone with information is urged to contact authorities.
The Council on American-Islamic Relations issued a statement saying investigators need to treat this as a hate crime.
"Hate and bigotry, against any group regardless of faith or background, cannot go unchecked, and we strongly condemn this blatant display of antisemitism," the group said.
LAUSD is conducting its own investigation into the vandalism and offering mental health counseling on campus for those affected.