(1) A person shall not operate a motorcycle with less than a 125 cubic centimeter engine, moped, farm tractor, or other self-propelled farm implement, nor shall a pedestrian, bicycle, except as provided in this section, or other nonmotorized traffic be permitted on a limited access highway in this state. Bicycles shall be permitted on paths constructed separately from the roadway and designated for the exclusive use of bicycles.

  (2) A person who violates this section is responsible for a civil infraction.