The process of excitation of Cherenkov electromagnetic radiation by a laser pulse in ion dielectric waveguide is investigated. Nonlinear electric polarization in isotropic ion dielectric medium and, accordingly, polarization charges and currents induced by a ponderomotive force of a laser pulse are determined. Frequency spectra of the excited wakefields in the infrared and microwave frequency ranges are obtained. The spatio-temporal structure of the wakefield in ion dielectric waveguide is obtained and studied. It is shown that the excited field consists of a potential polarization electric field, as well as a set of eigen electromagnetic waves of ion dielectric waveguide.