Minn. Stat. § 211B.18: DISQUALIFIED CANDIDATE NOT TO HOLD VARIOUS POSITIONS.

A candidate whose election to office has been set aside for a violation of this chapter or section 609.771 may not be appointed, during the period fixed by law as the term of the office, to fill a vacancy in that office. A candidate or other individual who is convicted of a violation of this chapter or section 609.771 may not be appointed, during the period fixed by law as the term of the office with respect to which the election was held and the offense was committed, to fill a vacancy that may occur in the office. An appointment to an office made contrary to the provisions of this section is void.

A candidate or other individual who is convicted of a violation of this chapter or section 609.771 is not qualified, during the period fixed by law as the term of the office with respect to which the election was held and the offense was committed, to fill a vacancy in an office for which the legislature may establish qualifications under article XII, section 3, of the Minnesota Constitution.