Minnesota voters can register at the polls on election day. From the Voter Registration website:

Registering on Election Day
If you are not registered to vote or need to update your registration information, you may do so at your local polling location on Election Day.  However, you are required to provide proof of residence when registering on Election Day. 

To register at your polling place on Election Day, you must have one of the following with your current name and address in the precinct to verify your residence:

• A valid Minnesota driver’s license, learner’s permit, Minnesota ID card, or receipt for any of these
• A valid student ID card including your photo, if your college has provided a student housing list to election officials
• A Tribal ID card that contains your picture and signature 
• A valid registration in the same precinct under a different name or address 
• A notice of late registration sent to you by your county auditor or city clerk
• A voter registered in the same precinct as you who can confirm your address with a signed oath

An employee of the residential facility where you live who can confirm your address with a signed oath