What are the names of the two Native American groups that were in Minnesota before the Europeans arrived?

Minnesota did not exist by that name before the USA was formed, long after European explorers arrived.

The area that later became Minnesota was occupied by the Ojibwe or Chippewa in the north and the tribes collectively called Sioux, who later became the Lakota, Nakota and Dakota. Before 1700 these Sioux tribes were in the area of Lake Mille Lacs and the Blue Earth and Cannon Rivers in the southern half of Minnesota.

Only after the arrival of Europeans did some of the Sioux tribes move west into the areas that later became North and South Dakota.