Purpose: This study investigated the ability of children with ASD, including the minimally verbal subgroup, to perceive angry, neutral, and happy prosody in low-pass filtered speech when provided with a structured training paradigm. Methods: 13 children with ASD and 21 TD children completed the experimental task and two additional measures (nonverbal cognitive abilities, social responsiveness deficits) for regression analyses. Results: The ASD group recognized prosodic conditions significantly less accurately than the TD group, and took significantly longer times to recognize all sentences compared to the TD group. Angry prosody was consistently the most difficult to recognize across groups. Nonverbal cognitive abilities is a significant predictor variable for successful recognition of neutral and happy prosody; although low nonverbal cognitive skills do not preclude minimally verbal children with ASD from accurately perceiving affective prosody. Conclusions: The present study shows it is possible for minimally verbal children with ASD to successfully participate in experimental research using judgment tasks when provided with appropriate training.