We describe the evaluation of response properties using multiresolution multiwavelet (MRMW) basis sets. The algorithm uses direct projection of the perturbed density operator onto the zeroth order density operator on the real space spanned by the MRMW basis set and is applied for evaluating the polarizability of small molecules using Hartree-Fock and Kohn-Sham density functional theory. The computed polarizabilities can be considered to be converged to effectively complete space within the requested precision. The efficiency of the method against the ordinary Gaussian basis computation is discussed.