Most, if not all, states in the USA have adopted the Interstate Compact on Drivers Licenses, a uniform statute, with minor variations. What that means is, almost always, whatever happens to your drivers license in one state will happen to it as well in another state (unless you take some legal action to prevent it - sometimes possible).
In general, if Michigan wants you to do certain things to reinstate your drivers license or right to drive, based upon something that happened in Michigan, then the Minnesota Department of Public Safety will honor that and also take away the right to drive in Minnesota and a Minnesota Drivers License. If it was a DWI in Michigan, the most practical solution would probably be to pay the fee and get the Michigan right to drive reinstated, then get a Minnesota drivers license. You can call the drivers license agencies in both states to confirm what you need to do, and seek reassurance that if you do, your license should be reinstated.
The short answer is that you are stuck paying this fee. If you ignore it, it will likely cause problems the next time you have to renew your MN driver's license. You could try to wait until MN says something, then pay it, but sometimes that can create a bigger mess to unravel. The best thing to do is suck it up and pay the fee, unfortunately. You could also consult with a Michigan attorney to see if they know of any ways around this fee or to get a reduction. Maybe they have a set up where you can take a safe driving course in exchange for a fee reduction or something like that.
Sign up to receive a 3-part series of useful information and legal advice about DUIs.