The legal drinking age in Minnesota is 21.
Off sales of liquor are restricted to licensed liquor stores. Liquor is only sold in liquor stores. Not supermarkets as you may be used to from other states, or gas stations as Wisconsin does. Some supermarkets operate their own liquor store right next door to their food supermarket, notably Trader Joe's.
You can't buy alcohol from a liquor store on a Sunday in Minnesota. Liquor stores are closed on Sundays, and also Thanksgiving Day, Christmas Day, and liquor stores must close at 8 p.m. on Christmas Eve.
Liquor stores can only open from 8 a.m. until 10 p.m., Monday through Saturday. Some cities restrict liquor store opening hours further - Minneapolis liquor stores may open these hours, but St. Paul liquor stores close at 8 p.m. Monday through Thursday, and are open until 10 p.m. on Friday and Saturday.
Some cities in Minnesota don't permit privately owned liquor stores. Instead, the city operates one or more liquor stores, and uses the profits for public projects. Among the Cities in the Minneapolis-St. Paul Metro Area with only city-run liquor stores are Brooklyn Center and Edina.
3.2 beer is less strictly regulated. It can be sold in grocery stores, and it can be sold on Sundays.
High alcohol spirits like Everclear are illegal in Minnesota.
Buying liquor from Wisconsin. Minnesota's liquor laws are starkly different from neighboring Wisconsin. Wisconsin sells beer, wine and spirits on Sunday, and you can buy it in supermarkets and even gas stations. Everclear can be sold in Wisconsin. And yes, you can drive to Wisconsin on Sunday and buy liquor to bring home.