Authorities described the shooting inside the Mall of Louisiana in Baton Rouge as a confrontation between two groups of people and not a random attack.
Police Chief TJ Morse said five people were in custody and there was no ongoing threat to the public.
Morse did not immediately say what set off the shooting at the mall in the Louisiana capital.
The shooting began when the two groups argued inside the food court and started shooting at each other, Morse said.
The chief made public appeals for witnesses to come forward with any video of the shooting.
Dozens of police cars still were clustered in the parking lot, multiple helicopters hovered overhead and armed officers in bulletproof vests patrolled the area.
Mall spokesperson Lindsay Kahn called it a "frightening day" for everyone there and said the mall would not reopen on Thursday.
Kennedy Barnum, 22, said she had gone to the mall to get lunch at the food court when she heard a woman on the phone outside say, "I'll call you back. There's an active shooter in the mall."
Within five minutes, Barnum said, law enforcement had swarmed the mall. She saw people running and crying, including one girl she described as "hysterical."
"We spoke to a security guard there and she told us that there was an active shooter there, people were shot and injured, and we should leave immediately," Barnum said.
It's at least the second high-profile case of gun violence in Louisiana this week.
A father fatally shot eight children, including seven of his own, in an attack on his family on Sunday that stretched across two houses in a Shreveport neighbourhood. Two women, including the gunman's wife who was the mother of their children, were critically wounded.
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