Gov. Tim Walz announced the new guidance Monday.
The school was planning to move to remote learning after Thanksgiving.
The senator says she didn't have close contact with the person who tested positive, but said she would quarantine and get tested anyway.
The university is imposing a campus quarantine until Sept. 22.
Minnesota was on the list for one week.
Minnesota has now reached the COVID-19 quarantine threshold, Gov. Andrew Cuomo announced.