You have the right to a habitable apartment and rodent infestation likely breaches the covenant of habitability given by the landlord. Ideally, you would bring a rent abatement action in the court of the county where the property is located. You pay your rent into court and get to stay in the property until the problem is cured or the court may give your rent back if not fixed. Alternately you can simply give written notice of a breach of the lease, allow the time to cure as may be provided, and if not fixed, move out. This second option may result in the landlord suing you for unpaid rent claiming he was not in breach of the lease. Documentation in either option is key. You could also call the city health inspector or city rental licensing department to come out and view the property.
Minnesota courts will award tenants reduced rent (and maybe back rent) in situations where the landlord violates what is referred to as the implied covenant of quiet enjoyment, and the presence of pests in the apartment has been found to be a violation of this covenant. You have a couple of options. First, you can start paying your rent to the court until the landlord fixes the problem. Second, you can bring what is called a tenant remedy action and attempt to get a portion of your rent back and potentially have your rent reduced. You may even be able to have the court terminate your lease. There are express instructions on the Minnesota State court website on how to do this, and forms are included. Third, you could attempt to negotiate with your landlord and tell him or her that he or she has violated the lease. Finally, you could just stop paying rent. This last option, however, is not a great idea. Although you will be able to bring back rent to the court if the landlord attempts to evict you, the court will not look favorably on this.
Disclaimer: please note that an attorney-client relationship will not be formed by this answer. Rather, I am providing some thoughts on the issues generally, based on my experience and the facts described in the question.