A statistical description of hydrodynamic processes for molten salts is proposed taking into account polarization effects caused by the deformation of external ionic shells. This description is conducted by means of the Zubarev nonequilibrium statistical operator method, appropriate for researches of both strong and weak nonequilibrium processes. The nonequilibrium statistical operator and the generalized hydrodynamic equations that take into account the polarization processes are acquired for the ion-polarization model of ionic molten salts when the nonequilibrium averaged values of densities of ions number, their momentum, dipole momentum, and total energy are chosen for the reduced description parameters. A spectrum of collective excitations is investigated within the viscoelastic approximation for the ion-polarization model of ionic melts.