Dynamics of polarization relaxation at the solid-liquid interface is investigated theoretically by using time dependent density functional theory. The time dependence of the building up of solvent polarization next to a newly charged solid surface is calculated by solving both Markovian and non-Markovian equations of motion for density and momentum variables. The initial inhomogeneity of the medium is taken into account and it is calculated by using a weighted density functional theory. Explicit numerical results are obtained for the relaxation of solvent polarization at varying distances from the solid surface and the dynamics of interfacial relaxation is compared with that of the bulk, A slowing down of the rate of relaxation is found for interfacial molecules. However, the relaxation rate changes nonmonotonically with distance from the surface which can be attributed to the layering of solvent molecules in the interfacial region.