We study the effects of excitons and their optical excitation or radiative decay in the photoinduced conduction intersubband transitions of undoped quantum wells. We show that the excitonic effects, in general, can strongly influence these transitions by making their dipole moments strongly dependent on the hole subband dispersions and quantum well strain. This allows spinor mixing of a hole subband to significantly suppress a photoinduced intersubband transition when this subband is strongly nonparabolic and/or is about to crossover another subband. Compared to those happening in the absence of any interband transition, however, we show that when the photoinduced intersubband transitions are accompanied with the optical excitation or radiative decay of excitons (excitonic interband transitions) their electric dipole moments can suffer an additional suppression. We attribute this effect to the influence of the correlation between the electron and hole positions in the photoinduced intersubband transitions and the way it depends on the excitonic interband transitions. In all cases, however, our results suggest that ignoring the effects of excitons in the conduction intersubband transitions of undoped quantum wells, i.e., considering only electron wave functions, could lead to an unrealistic overestimation of their dipole moments.