Police in Los Angeles arrested a man who took hostages and barricaded himself inside a Trader Joe's grocery store on Saturday, ending a three-hour standoff during which he fatally shot a woman, authorities said.

The man, who was chased by police after he was suspected of repeatedly shooting his grandmother and another woman in a separate part of the city, crashed his car outside the Trader Joe's, where he exchanged gunfire with police and entered the crowded store.

Police officers use a mirror to see inside a Trader Joe's store in the Silver Lake neighbourhood of Los Angeles on Saturday during the standoff. (Christian Dunlop via AP)

He was shot in the arm and talked with police over the phone to negotiate a surrender, Mayor Eric Garcetti and police told a news conference.

The man, 28 and not named by police, emerged from the store and was surrounded by police.

"Inside the Trader Joe's the suspect shot a female victim. She was pronounced dead at scene," police said on Twitter.

He then proceeded to hold multiple victims hostage within the location. Through the hard work of multiple LAPD entities, the suspect walked out of the location, and asked that he put handcuffs on himself, and was taken into custody. —@LAPDHQ

Once he was in custody, about 20 people who were in the store could be seen spilling out on to the street.

The woman has not officially been identified, but ABC News named her as Melyda Corado, the store manager, citing family sources.

"The suspect at the end asked for handcuffs. He handcuffed himself and then released himself into the custody of L.A. police," Garcetti said.

Supermarket employees hug after being evacuated from the store by Los Angeles police after a gunman barricaded himself inside. (Damian Dovarganes/Associated Press)

During the standoff, aerial footage from TV stations NBC Los Angeles and CBS Los Angeles showed people leaving a store window using a rope ladder and police carrying children to safety through a parking lot in the city's Silver Lake neighbourhood.

Trader Joe's employee Zach Johnston was among those who escaped shortly after hearing gunshots.

"I was in the back room and all of a sudden I started to see customers spilling through the door going to the back room."

"I immediately heard some gunfire, like four pops," he said.

The suspect eventually crashed his car outside of the Trader Joe's supermarket and then ran into the store, police say. (Christian Dunlop via AP)

Johnston and about 15 customers and co-workers ran out a back door to safety, he said.

More than an hour after the standoff began, a few hostages were shown on TV leaving the store through the front door. Some said they had hidden in employee areas in the back of the store.

U.S. President Donald Trump said he was watching the situation closely.

"Active barricaded suspect. L.A.P.D. working with Federal Law Enforcement," Trump wrote on Twitter before the arrest.