Possibility of measuring invisible Higgs boson decays is studied for CLIC running at 380 GeV and 1.5 TeV. The analysis is based on the WHIZARD event generation and fast simulation of the CLIC detector response with DELPHES. Expected limits on the invisible decays of the 125 GeV Higgs boson are estimated, as well as the cross section limits for production of an additional neutral Higgs-like scalar, assuming its invisible decays, as a function of its mass. Extracted model-independent branching ratio and cross section limits are then interpreted in the framework of the vector-fermion dark matter model to set limits on the mixing angle between the SM-like Higss boson and the new scalar of the "dark sector".