Minnesota states that any person who, “Makes a bet,” presumably in any way not specifically authorized by the state, has committed a Misdemeanor.

Even with that, the law does not prescribe any sort of specific penalty for doing that or discuss what class of Misdemeanor that it might be.
We can find no instance...
...of anyone being charged merely for acting as a player and this is especially true when it comes to online gambling. Operating an illegal sportsbook seems to be the most serious thing anyone can do in the State of Minnesota, is considered a Gross Misdemeanor. It can carry fines of up to $3,000 and imprisonment for up to a year.
The same penalty that could apply to illegal bookmaking also applies to operate an “Illegal Gambling House,” in general, which would also presumably include operating an online casino that caters to people within or without the state.
The biggest case that we discovered, which you can read more about here.
Involved twelve arrests for the conducting of an illegal lottery.
While online gambling might technically violate the law, there have been no arrests that we can find or convictions, and pragmatically, it would be shocking for law enforcement to ever come to discover it.
For that reason...
... most online casinos who operate in the United States at all also operate within the State of Minnesota, and many of them are listed below: