In the model of effective masses and rectangular potentials, the effect of a hydrogen-like donor impurity on the energy spectrum, electron wave functions and oscillator strengths of intraband quantum transitions in a quantum dot–quantum ring semiconductor nanostructure (GaAs/AlxGa1-xAs) is studied theoretically. The stationary Schr€odinger equation for an electron interacting with an impurity cannot be solved analytically exactly. For its approximate solution, the unknown wave functions are sought in the form of an expansion over a complete set of cylindrically symmetric wave functions in the nanostructure without impurity, and the electron energy is found by solving the corresponding secular equation. The dependences of the energy spectrum, the binding energy of the electron with the impurity and the oscillator strengths of the quantum intraband transitions on the geometric parameters of the nanostructure are analyzed.