Energy spectrum, wave functions and binding energies of the electron to the donor impurity ion located in the center of a multilayer spherical quantum dot (MSQD) consisting of a core (GaAs) and two spherical shells (AlxGa1–xAs and GaAs) were studied within the effective mass approximation. Based on the exact wave functions of the electron expressed in terms of Coulomb functions of the first and second kind, the spectral dependences of the photoionization cross section of the impurity (PCS) and the intersubband optical absorption coefficient (OAC) for various geometric dimensions of the nanostructure were calculated. It is shown that the decrease in the width of the external potential well changes the localization of the electron in the nanosystem which significantly affects the binding energy of the electron with the impurity, photoionization cross section and interband absorption coefficient. The position of the PCS peak associated with the quantum transition of an electron from the ground state to the 1p0 state shifts to the region of higher energies, and its height decreases. At the same time, the height of PCS peaks associated with quantum transitions to higher excited states (2p0, 3p0) increases. The presence of impurities and changes in the MSQD size significantly affect the intersubband absorption coefficient. Decrease of the external potential well width in the absence of impurities leads to a monotonous increase in OAC through the first excited state, and in the presence of a central impurity, absorption through states with higher energy increases. Obtained results enable prediction of the specifics of the effect of the magnetic field on the optical properties of MSQD with two potential wells.