The possibilities of manufacturing batteries with Nafion 117 membranes in the Na+-form intercalated by mixtures of non-aqueous organic solvents used both as an electrolyte, separator, and binder were investigated. Electrochemical stability of various organic solvent mixtures based on N,N-dimethylacetamide, ethylene carbonate, propylene carbonate, and tetrahydrofuran were characterized. It was shown that a sodium battery based on a Nafion-Na membrane intercalated by mixture of ethylene carbonate and propylene carbonate with a Na3V1.9Fe0.1(PO4)3/C positive electrode is characterized by a discharge capacity of ≈110 mAh·g−1 (current density of 10 mA·g−1) at room temperature and shows the ability to cycle without degradation during 20 cycles. Batteries with Nafion membrane electrolytes, containing N,N-dimethylacetamide, were characterized using capacity fading during cycling, which is due to the interaction of N,N-dimethylacetamide and a negative sodium electrode.