In this paper, we report on the experimental observation of light-induced anisotropy (the optical Kerr effect) due to third-order nonlinear dielectric susceptibility (3) in a nanocomposite material consisting of CdSe quantum dots in a phosphate glass matrix. The signs and values of the off-diagonal components of the tensor (3) are determined using z-scanning techniques and nonlinear ellipsometry. It was shown that the nonlinear response contains three time components, the fastest of which does not exceed 20 ps, the average has an exponential form and amounted to 90 11 and 38530 ps for different samples, and the longest nonexponential and amounts to times of the order of a few nanoseconds. The switching of an optical signal with a time not exceeding 20 ps is demonstrated.