MN and WI no longer have a reciprocal tax agreement.  AS such, for any work you physically do in MN, you have to pay taxes to MN on that MN-located income. 

Assuming that this is a temporary job in MN, or that you spend most of your nights during the year in WI, then you file a nonresident tax return in MN for just that MN income, and also a Resident tax return in WI for ALL your income from everywhere (including MN)....but, WI then allows you to take a credit on the WI tax return for the taxes that MN kept (with some math handwaving if the tax rates don't match...they don't).

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Beyond that...it really depends on your working situation.  IF you are renting an Apt in MN, and are expecting to spend more than half the nights of the year in MN for some years to come too....then MN may consider you an actual MN resident...and you may be forced to become a MN resident and file part-year tax returns for both MN&WI for the first year working there, and in future years, be a considered a full resident of MN  and a non-resident of WI.  (only significant exceptions are college students from another state, or persons/spouses in the military from other states).

Determining if that may fit your situation is a legal/tax situation none of us here can really advise you on...and you should seek a discussion for advice from a local MN enrolled tax agent/professional (NOT a seasonal storefront) to discuss the ramifications of your living/working situation, and the details about what MN may require of you re: taxes and state residency.