Austin Police Chief Lisa Davis told a news conference the suspect is a man in his 30s with "a mental health history."
Davis said the man fled the scene in a stolen car, wrecked that car then stole another from a dealership. He was captured in south Austin, where he was taken into custody.
She said responding officers found three people who had been shot in the Target parking lot.
Austin-Travis County EMS Chief Robert Luckritz said two people were pronounced dead at the scene and one person was taken to a hospital where they were pronounced dead.Â
He said another person was treated on the scene for unrelated injuries.
"This is a very sad day for Austin. It's a very sad day for us all and my condolences go out to the families," Davis said.
She said she had no information to release about the victims.
Target didn't immediately respond to a request seeking comment.
The shooting came amid back-to-school shopping ahead of the upcoming school year.
"This is a devastating situation, and my heart is with the victims and their families," Austin Mayor Kirk Watson said in a message on X.
"While this remains an active and ongoing investigation, what I'll say is that this was a sickening, cowardly act of gun violence."
At a Jiffy Lube that shares its parking lot with Target, employees hunkered down and locked the store doors as soon as they became aware a shooting was taking place.
Paul Smith, an employee at the auto store, said he saw people running from their cars in the parking lot in a panic.
"I had just gotten back from the Target like a minute before," he said.
The Target shooting comes just over two weeks after an attack at a Walmart store in Michigan. A man stabbed 11 people at the store in Traverse City on July 26 and has been charged with terrorism and multiple counts of attempted murder.
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