We have used the effective-mass approximation and a variational procedure in the study of internal transitions associated with 1s-, 2p-, 3p-, and 4p-like magneto-exciton confined states in GaAs–(Ga, Al)As quantum wells, under a magnetic field applied in the growth direction. Theoretical results were obtained as a function of the applied magnetic field and for several well widths. The calculated far-infrared intraexcitonic transition energies are found in good agreement with recent experimental measurements obtained via a highly sensitive optically detected resonance technique.