The photon-induced dimuon production e(+)e(-) -> e(+)gamma gamma e(-) -> e(+)mu(+)mu(-)e(-) at the CLIC is studied in the framework of three models with extra dimensions. The electron beam energies 750 GeV and 1500 GeV are considered. The total cross sections are calculated depending on the minimal transverse momenta of the final muons. The sensitivity bounds on the parameters of the models are obtained as functions of the CLIC integrated luminosity. (C) 2020 Published by Elsevier B.V.