The 16-month-old boy was rescued by a parent dropping off a different child at the day care residence.
The woman fled in her minivan, striking two people, before attempting to take her own life by jumping off a bridge, but was stopped by bystanders.
Police have not released a possible motive, but say that the child is "doing fine".
Minneapolis Assistant Police Chief Kris Arneson said that the woman is now being evaluated at a local hospital.
"It's horrific, horrific," Ms Arneson said of the assault.
"We never want children to be injured. That's part of reason we call in our chaplains. It's a horrific scene for officers to encounter," she added.
The hit-and-run victim, who was dragged for several blocks, has broken bones and cuts but is expected to survive, Ms Arneson said.
A cyclist was also hit by the same minivan.
At least six investigators are working on the case, including detectives from the homicide and crimes against children units.
Police declined to provide the suspect's name.
There were fewer than six children in the nursery at the time of the attack, Ms Arneson said.
A nursery worker intentionally hung a one-year-old child in her care, police say.