Police were responding to a report of a shooting at the Trader Joe's near Hyperion Avenue and Silver Lake Boulevard in Silver Lake Saturday afternoon, CBS LA reports.
Los Angeles police have surrounded a supermarket where a suspect barricaded himself, with United States media describing it as a possible hostage situation.
Officers opened fire on the vehicle and then a pursuit ensued, police said. Customers ran out of the store, he added.
LAPD said the man shot his grandmother and girlfriend in South L.A. before leading police on a pursuit and crashing his vehicle outside the store.
After previously tweeting about "an active police incident", the LAPD tweeted that an individual had "barricaded themselves" at the chain grocery story. Los Angeles Fire Department spokeswoman Margaret Stewart indicated that a female, 20, was transferred to the hospital with injuries, according to CNN.
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Photos posted on social media show a auto crashed outside the store entrance as heavily armed police swarm the area.
She said employees eventually let shoppers out. Authorities are trying to communicate with the suspect to try to bring the situation to a peaceful conclusion, police said.
LAPD said SWAT teams were on the scene to try to "bring a swift resolution to this incident".
Aerial video shot from a helicopter showed armed officers carrying shields outside the store and a man walking out with his hands up.