A full-field perturbation approach is modified for an ice-covered ocean and applied to estimating narrowband long-range reverberation caused by roughness of the ice-water interface. First-order approximation of the approach is used which requires the roughness amplitudes be small compared to the acoustic wavelength. To obtain the zeroth-order Green's function and transmission loss field used in the reverberation model, elastic parabolic equation solutions are generated in range-independent environments. Ice is represented by an isospeed layer on top of a linear transition layer. Effects of ice properties are discussed and demonstrated by comparing reverberation calculated for different ice layer thicknesses and wave speeds for typical ice values.