Sheriff's deputies were called at lunchtime on Friday to an apartment complex in a gated community near a golf course in a usually quiet neighbourhood of suburban Memphis.
They took the mother into custody after finding the children's bodies.
Officials have not released the ages of the children, but deputies said they were "babies".
Shelby County Sheriff Bill Oldham said: "This is an egregious act of evil that has shocked us to our core.
"I will never understand how anyone can do this."
He did not specify whether the mother had stabbed the children and said it was unclear if she had any mental health issues.
The sheriff added: "One of the most difficult questions in any investigation is always, 'Why did this happen?'"
The Memphis Commercial Appeal reports that another child, a seven-year-old, escaped the apartment.
The newspaper reported that the mother was a 29-year-old woman who was booked into the Shelby County Jail, though no charges were listed.
The state Department of Children's Service said it had no record of interaction with the deceased children.
Neighbour Sean Ahearn said he often saw the "very open and friendly" children playing in the front yard.
He said they all appeared to be under age six and they liked to pet his dog.
Another resident, Patricia Johnson, burst into tears when she learned of the deaths.
"I can't fathom that," she said. "What would babies do to make you do that?"
Ms Johnson told reporters she would be praying for the whole family.
"Something went wrong, drastically wrong," she said.
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