LAPD have warned the public to stay away from the area, and television footage from the scene has shown shoppers scrambling to get out of windows.
Police were called to the scene at around 3:30pm local time (11:30pm BST).
The LAPD confirmed the incident on Twitter, saying: “We can confirm that there is an active barricaded suspect within a Trader Joes in Silverlake.
“An active tac-alert has been declared to ensure all resources necessary will be available.
“Please continue to stay clear of the area.”
The incident began with an earlier shooting in which a young woman and an elderly woman were shot at.
An LAPD officer told a media briefing the suspect shot at his grandmother and another woman before fleeing in his grandmother’s car with the wounded younger female.
It is currently unknown how many people are trapped inside the supermarket.
An LAPD officer said: “We know we have people inside. We don’t know how many.”
President Donald Trump has said he is “watching” the situation.
He posted on Twitter: “Watching Los Angeles possible hostage situation very closely.
“Active barricaded suspect.
“L.A.P.D. working with Federal Law Enforcement.”
One witness told local television the suspect was shooting “as he came around the corner” in his car.
Derek Anthony told NBC4 he saw the end of a car chase: “The car had heavy damage, had flat tyres and (the suspect) was still careening around the corner with all the police behind him, and he was shooting his gun as he came around the corner.”
Eighteen ambulances and more than one hundred firefighters are at the scene, LA Fire Department confirmed.
More to follow