Citation: MINN. STAT. 346.155
In Minnesota you need a fur farm registration to breed and sell fox.
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Subd. 3. Fur-bearing animal. “Fur-bearing animal” means a fox, mink, fitch, chinchilla, karakul, marten, nutria, or fisher that is the second or later generation raised in captivity.
Subd. 4. Fur farmer. “Fur farmer” means a person engaged in breeding, raising, producing, and marketing fur-bearing animals or the products of fur-bearing animals.
Fox are also listed as small game and cannot be possessed as small game are defined as Protected wild animals.
97A.501 WILD ANIMALS: GENERAL RESTRICTIONS.
Subdivision 1. General restrictions. A person may not take, buy, sell, transport, or possess a protected wild animal unless allowed by the game and fish laws.
Plus no one may own a wild animal which would include fox by their definition so the only way to have one as written would be to have the fur farm registration.
They are kind of strict about wild animals (this might only apply to natives but it seems to read as any wild animal so could apply to exotics as well since it does not say native to or living in the state like most native laws do.
Subd. 55. Wild animals. "Wild animals" means all living creatures, not human, wild by nature, endowed with sensation and power of voluntary motion, and includes mammals, birds, fish, amphibians, reptiles, crustaceans, and mollusks.
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A person may not acquire a property right in wild animals, or destroy them, unless authorized under the game and fish laws, sections 84.091 to 84.15, or sections 17.47 to 17.498.