Representation of amplitude modulation (AM) has been characterized by neurophysiological and psychophysical modulation transfer functions (MTFs). Our recent computational study demonstrated that a deep neural network (DNN) trained for natural sound recognition serves as a good model for explaining the functional significance of neuronal MTFs derived physiologically. The present study addresses the question of whether the DNN can provide insights into AM-related human behaviours such as AM detectability. Specifically, we measured “psychophysical” MTFs in our previously developed DNN model. We presented to the DNN sinusoidally amplitude-modulated white noise with various AM rates, and quantified AM detectability as d′ derived from the model’s internal representations of modulated and non-modulated stimuli. The overall d′ increased along the layer cascade, with human-level detectability observed in the higher layers. In a given layer, the d′ tended to decrease with increasing AM rates and with decreasing AM depth, which is reminiscent of a psychophysical MTF. The results suggest that a DNN trained for natural sound recognition can serve as a model for understanding psychophysical AM detectability. Since our approach is not specific to AM, the present paradigm opens the possibility of exploring a broad range of auditory functions that can be evaluated by psychophysical experiments.