The physicochemical properties and ionic conductivity of Nafion polymer membrane in sodium form plasticized with such organic solvents as ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC) and their ternary mixtures were studied. According to the results of gravimetry, simultaneous thermal analysis, IR spectroscopy, small-angle X-ray scattering, voltammetry, and impedance spectroscopy, it was shown that the optimal plasticizer for Na-Nafion membrane among the studied systems is a ternary mixture with the composition EC/PC/DMC = 0.45/0.45/0.1. The polymer electrolyte based on Na-Nafion, plasticized with this ternary mixture, despite the lower electrochemical stability compared to the membrane swollen with EC, has the highest swelling degree of 31% and the ionic conductivity of 0.08 mS cm−1 at 20 °C, which is maintained even at −60 °C (6 × 10−8 S cm−1). The obtained values are comparable with the conductivity of the lithium form of Nafion. The possibility of using a membrane based on the sodium form of Nafion as an electrolyte in sodium and sodium-ion batteries was shown.