As far as I know there are zero state regulations in Minnesota regarding regulation of pet reptiles.

Hots, crocodilians, giant constrictors, and everything else are good to go.

Many cities and towns however have restrictions in place. I know that Northfield (the town where I went to college) specifically restricts venomous reptiles.

I don't know much about other exotic pets in Minnesota, but I believe that there are regulations that specifically mention native wild animals (wolves, raccoons, skunks, porcupines, etc). However I don't know what those regulations say.