Another four children were injured by the 25-year-old man who entered the creche at around 09:00 local time (12:00 GMT) on Wednesday.
Hospital officials said those injured were all under the age of three.
Police told local media that the attacker had surrendered and that he had been taken into police custody.
The governor of Santa Catarina state – where Blumenau is located – has declared three days of mourning.
President Luiz Inácio Lula da Silva tweeted that “there is no greater pain than that of a family that loses its children or grandchildren, even more so when it’s through an act of violence against innocent children who can’t defend themselves”.
