We present a polarizable water model for the Dissipative Particle Dynamics (DPD) method. Employing long-range electrostatics and Drude oscillators, we calibrate the model using the compressibility and the dielectric constant of water. We validate the model by sampling the dielectric properties of solutions of sodium chloride at various concentrations. Additionally, we apply our model in equilibrium and electroporation simulations of a pure dipalmitoylphosphatidylcholine (DPPC) bilayer, a pure cholesterol domain and a mixed DPPC-cholesterol membrane in polarizable water. Finally, we simulate the transport of a short DNA segment through a DPPC bilayer driven by an external electric field. The new water model is suitable for the DPD simulations of systems where polarization effects play an essential role.