In the model of effective masses and rectangular potentials, the influence of a homogeneous electric field on the energy spectrum, electron wave functions, and oscillator strengths of intraband quantum transitions in a semiconductor (GaAs/AlxGa1-xAs) quantum dot-quantum ring nanostructure is theoretically investigated. In the presence of an electric field, the stationary Schrödinger equations for quasiparticles are not analytically solved. For their approximate solution, the unknown wave functions are sought in the form of an expansion over a complete set of cylindrically symmetric wave functions, and the electron energy is found from the solution of the corresponding secular equation. It is shown that the electric field significantly affects the localization of the electron in the multilayer nanostructure. In this case, both the electron energy and the strength of the oscillators of intraband quantum transitions depend nonmonotonically on the magnitude of the electric field strength.