A man has been arrested on suspicion of murder after a deadly shoot-out and hostage situation at a Los Angeles supermarket.

Police said Gene Evin Atkins, 28, is being held after a woman was shot and killed in the incident at the Trader Joe’s store in the Silver Lake area on Saturday.

No hostages were seriously hurt before the attacker handcuffed himself and surrendered about three hours later.

The woman who died has been identified as 27-year-old Melyda Corado. Her brother Albert Corado said on Twitter that she worked at Trader Joe’s.

“I’m sad to say she didn’t make it. My baby sister. My world,” he tweeted.

Investigators have not confirmed if her death sparked Atkins’s arrest on a murder charge.

Officials say Atkins shot his grandmother seven times and wounded another woman, who he forced into a car. Officers tracked the car, gave chase and exchanged gunfire with the man, who crashed into a pole outside the supermarket and then ran inside.

Atkins’s grandmother is in hospital in a critical condition, while the woman forced into a car suffered minor injuries.

Frightened customers and workers dived for cover as police bullets fired at the man shattered the store’s glass doors.

Some people inside the supermarket climbed out windows, and others barricaded themselves in rooms as scores of police officers and firefighters and 18 ambulances converged on the scene and prepared for mass casualties.

Heavily armed officers in riot gear stood along the side of the store and used mirrors to look inside as hostage negotiators tried to coax the man into freeing his 40-50 hostages and surrendering.

At about 6.30pm local time, the man agreed to handcuff himself and walked out the front door, surrounded by four of the hostages.

Mayor Eric Garcetti congratulated police and firefighters for their work, adding: “The heroism that was shown today was second to none, and the teams that were able to respond, secure the perimeter and engage in conversation with the suspect no doubt saved lives today,” he said.

Fire officials said six people, ranging in age from 12 to 81, were taken to hospital. None had been shot, and all were in fair condition.

Among those caught up in the incident was 91-year-old Don Kohles, who was walking into the supermarket when he saw “two police cars coming like a bat out of hell” and the man crashed into the pole.

The driver got out, and police started firing at him as he ran towards the supermarket. Mr Kohles said he hurried inside, and he and others took cover as the man ran in.

“Those bullets went right over the back of me as he was running right down the main aisle,” Mr Kohles said.

Police officers use a mirror to see inside a Trader Joe’s store Police officers use a mirror to see inside the Trader Joe’s store (Christian Dunlop via AP)

Christian Dunlop was on a corner near the store when he saw four people run out. One person, an employee, was dragging an injured woman by the hands. “She appeared lifeless,” Mr Dunlop said.

He then saw about five employees hang out a second-floor window and drop to the ground and about 15 other people run to safety from the back of the store. Among them was a police officer carrying a small child, he said.

“I know all the employees,” Mr Dunlop said. “I see them all the time. My heart was just racing and thinking about all the endless possibilities.”