The move came as the Australian parliament fast-tracked legislation to toughen penalties for those found tampering with food.
During the shootout, the suspect was wounded in the arm, Mayor Eric Garcetti said, adding that one woman was shot in the store and later declared dead at the scene.
Police later stormed the supermarket in the small town of Trebes and Interior Minister Gerard Collomb said on Twitter that the attacker had been killed.
Supermarket chain Lidl has apologised for airbrushing Christian crosses out of images of the Greek island of Santorini on some of its food packaging, after being hit by criticism on social media.
A 26-year-old failed asylum seeker who carried out a deadly knife attack in a Hamburg supermarket likely had a "radical Islamist" motive, German prosecutors said on Monday.
A man who opened fire near a supermarket west of Paris and seriously injured two people is an incident not at first sight considered to be a possible act of terrorism ...