Neural tracking of the low-frequency temporal envelope of speech has emerged as a prominent tool to investigate the neural mechanisms of natural speech processing in the brain. However, there is ongoing debate regarding the functional role of neural envelope tracking. In this context, our study aims to offer a novel perspective by investigating the critical brain areas and behavioral skills required for neural envelope tracking in aphasia, a language disorder characterized by impaired neural envelope tracking. We analyzed an EEG dataset of 39 individuals with post-stroke aphasia suffering a left-hemispheric stroke who listened to natural speech. Our analysis involved lesion mapping, where left lesioned brain voxels served as binary features to predict neural envelope tracking measures. We also examined the behavioral correlates of receptive language, naming, and auditory processing (via rise time discrimination task) skills. The lesion mapping analysis revealed that lesions in language areas, such as the middle temporal gyrus, supramarginal gyrus and angular gyrus, were associated with poorer neural envelope tracking. Additionally, neural tracking was related to auditory processing skills and language (receptive and naming) skills. However, the effects on language skills were less robust, possibly due to ceiling effects in the language scores. Our findings highlight the importance of central brain areas implicated in language understanding, extending beyond the primary auditory cortex, and emphasize the role of intact auditory processing and language abilities in effectively processing the temporal envelope of speech. Collectively, these findings underscore the significance of neural envelope tracking beyond mere audibility and acoustic processes.