(Ca2+)-dependent pyrroloquinolinequinone (PQQ)-dependent methanol dehydrogenase (MDH) (EC: 1.1.2.7) is one of the key enzymes of primary C1-compound metabolism in methylotrophy. PQQ-MDH is a promising catalyst for electrochemical biosensors and biofuel cells. However, the large-scale use of PQQ-MDH in bioelectrocatalysis is not possible due to the low yield of the native enzyme. Homologously overexpressed MDH was obtained from methylotrophic bacterium Methylorubrum extorquens AM1 by cloning the gene of only one subunit, mxaF. The His-tagged enzyme was easily purified by immobilized metal ion affinity chromatography (36% yield). A multimeric form (α6β6) of recombinant PQQ-MDH possessing enzymatic activity (0.54 U/mg) and high stability was demonstrated for the first time. pH-optimum of the purified protein was about 9–10; the enzyme was activated by ammonium ions. It had the highest affinity toward methanol (KM = 0.36 mM). The recombinant MDH was used for the fabrication of an amperometric biosensor. Its linear range for methanol concentrations was 0.002–0.1 mM, the detection limit was 0.7 µM. The properties of the invented biosensor are competitive to the analogs, meaning that this enzyme is a promising catalyst for industrial methanol biosensors. The developed simplified technology for PQQ-MDH production opens up new opportunities for the development of bioelectrocatalytic systems.