No, as long as we’re talking about a push-pedal bike and not a motorbike. Minnesota DWI/DUI laws only criminalize driving, operating, or being in physical control of motor vehicles. Under Minnesota law, motor vehicles are those that are self-propelled or propelled by electric power obtained from overhead trolley wires, including motorboats in operation and off-road recreational vehicles. People have picked up DWI charges driving a Zamboni, a La-Z-Boy, a riding lawnmower, and a front-end loader, but interestingly those on a Segway or a motorized scooter had their charges thrown out. Long story short, any vehicle moved solely by human power, like a bicycle, is not considered a motor vehicle for DWI/DUI purposes.
If you’re planning to imbibe and bike, you need not worry about DWI charges. But you still need to obey all traffic laws, and if you’re weaving on your bike too much, for example, you could be cited for careless driving (a misdemeanor), even though you’re not driving a motor vehicle. Have fun, bike safely, and for Pete’s sake wear a helmet!