Those killed -- three boys and a girl -- were between the ages of 5 and 7, local police say.
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Jorginho Mello, the governor of the state of Santa Catarina, said on Twitter that a male suspect has been arrested.
A police officer told CNN Brazil that the suspect, age 25, is understood to have jumped over a wall into the playground of the Cantinho Bom Pastor day care center, before attacking the children.
He fled after teachers came to the children's defense, and later turned himself into police, according to the official.
Mello expressed his solidarity with the victims.
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"May God comfort the hearts of all families in this time of deep sorrow," he said.
President Luiz Inácio Lula da Silva also gave his condolences.
"There is no greater pain than that of a family that loses its children or grandchildren, even more so in an act of violence against innocent and defenseless children," Lula wrote on Twitter.
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