Rechargeable zinc–air batteries are deemed as the most feasible alternative to replace lithium–ion batteries in various applications. Among battery components, separators play a crucial role in the commercial realization of rechargeable zinc–air batteries, especially from the viewpoint of preventing zincate (Zn(OH)42−) ion crossover from the zinc anode to the air cathode. In this study, a new hydroxide exchange membrane for zinc–air batteries was synthesized using poly (2,6-dimethyl-1,4-phenylene oxide) (PPO) as the base polymer. PPO was quaternized using three tertiary amines, including trimethylamine (TMA), 1-methylpyrolidine (MPY), and 1-methylimidazole (MIM), and casted into separator films. The successful synthesis process was confirmed by proton nuclear magnetic resonance and Fourier-transform infrared spectroscopy, while their thermal stability was examined using thermogravimetric analysis. Besides, their water/electrolyte absorption capacity and dimensional change, induced by the electrolyte uptake, were studied. Ionic conductivity of PPO–TMA, PPO–MPY, and PPO–MIM was determined using electrochemical impedance spectroscopy to be 0.17, 0.16, and 0.003 mS/cm, respectively. Zincate crossover evaluation tests revealed very low zincate diffusion coefficient of 1.13 × 10−8, and 0.28 × 10−8 cm2/min for PPO–TMA, and PPO–MPY, respectively. Moreover, galvanostatic discharge performance of the primary batteries assembled using PPO–TMA and PPO–MPY as initial battery tests showed a high specific discharge capacity and specific power of ~800 mAh/gZn and 1000 mWh/gZn, respectively. Low zincate crossover and high discharge capacity of these separator membranes makes them potential materials to be used in zinc–air batteries.