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.
Public safety agencies responded in force, with an armored police vehicle parked outside the store and seven ambulances and dozens of law enforcement vehicles arriving on the scene.
The incident prompted a major police response.
Lopez said customers ran out of the Trader Joe's.
Twenty-two people are believed to be hiding in a closet and are now texting police.
A woman believed to have been shot was dragged away from the entry while unconscious.
As officers worked to evacuate people from the store, at least one person was seen with injuries.
A lockdown is happening with the entire area being evacuated.
The incident broke out at approximately 3:30 p.m. CBS News reported that the suspect had shot his grandmother and girlfriend in South L.A. before police pursued him to Hyperion Avenue in Silver Lake.
A gunman opened fire outside a Los Angeles-area Trader Joe's supermarket on Saturday and barricaded himself inside, police said.
TV helicopters showed police rescuing a group of children from the store, while other views showed people leaving through the front door with their hands up.
The suspect has been shot and is talking with police negotiators, NBC Los Angeles said.