Officer Bruce Borihanh says the man, in his mid-30s, suffered a non-life threatening gunshot wound at about 9:40 a.m. Tuesday at the 92nd Street Elementary School. He is hospitalized in stable condition.
Borihanh says the alleged shooter is the victim's girlfriend and the couple had been arguing. Her identity is known and she is being sought by officers.
The school was not locked down.
Los Angeles residents are voting in a mayoral primary and deciding a number of other city offices.