The collision occurred shortly before 1:30 p.m. at a shopping center in the Fairfax District. The parking lot is shared by a Trader Joe's grocery store, Mendocino Farms and Sidecar Doughnuts.
One victim was pronounced dead at the scene and four others were transported to a hospital, according to the Los Angeles Fire Department.
Aerial video showed firefighters attending to the injured at the scene, located across the street from a shopping mall.
The driver, a woman in her 80s, remained at the scene after the crash, a spokesperson for the Los Angeles Police Department said. No arrest was announced.
The cause of the crash was unknown.