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.

It follows a decision by Education Minister Peter Weir to reverse a long-standing departmental policy.
A circular sent to school principals on Wednesday removes any prohibition on using academic selection to decide what post-primary school pupils transfer to.
As a result primary schools can prepare pupils for the AQE and GL Assessment tests during normal class time.
Teachers allowed off the 'naughty step'
However, the education minister has decided against re-introducing a common, department-run 11-plus test, admitting there was not enough political support to bring back an official exam.
"I have been resolutely supportive of academic selection and, indeed,  the right of people to have academic selection," Mr Weir told the BBC's Good Morning Ulster programme.
"This is actually about providing freedom to schools. They now have the freedom to choose whether to prepare their pupils, what level of help and assistance they can give in terms of preparation tests."
He said his decision to allow primary schools to formally prepare pupils for unofficial tests was "reflecting the reality of what is happening out on the ground, rather than trying to pretend that essentially, testing does not exist".
However, Mr Weir said no school would be "compelled" to carry out the preparation.
The 11-plus exam, which used to determine entry into grammar schools, was abolished in 2008.
Unofficial exams have been used by many grammar schools to decide which pupils to admit since then, but primary schools were not allowed to help pupils to prepare for those.
Previous departmental guidance said that primary schools "should not facilitate unregulated entrance test arrangements in any way".
They were therefore prohibited from "supplying support materials, carrying out any preparation for unregulated tests during core teaching hours, offering afternoon coaching in exam technique, or providing familiarisation with a test environment".
Mr Weir has now changed that, meaning primary schools can help pupils prepare for the AQE and GL Assessment tests if they wish.
Mr Weir is the first DUP education minister since the establishment of the Assembly in 1998.
Only Sinn Féin had held the education post until this year, and all of their ministers had expressed opposition to academic selection.
A nursery worker intentionally hung a one-year-old child in her care, police say.
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Primary schools in Northern Ireland are now free to prepare pupils for unregulated transfer tests.