Predictive modeling approaches are enabling progress toward robust and reproducible brain-based markers of neuropsychiatric conditions by leveraging the power of multivariate analyses of large datasets. While deep learning (DL) offers another promising avenue to further advance progress, there are challenges related to implementation in 3D (best for MRI) and interpretability. Here, we address these challenges and describe an interpretable predictive pipeline for inferring Autism diagnosis using 3D DL applied to minimally processed structural MRI scans. We trained 3D DL models to predict Autism diagnosis using the openly available ABIDE I and II datasets (n = 1329, split into training, validation, and test sets). Importantly, we did not perform transformation to template space, to reduce bias and maximize sensitivity to structural alterations associated with Autism. Our models attained predictive accuracies equivalent to those of previous machine learning (ML) studies, while side-stepping the time- and resource-demanding requirement to first normalize data to a template. Our interpretation step, which identified brain regions that contributed most to accurate inference, revealed regional Autism-related alterations that were highly consistent with the literature, encompassing a left-lateralized network of regions supporting language processing. We have openly shared our code and models to enable further progress towards remaining challenges, such as the clinical heterogeneity of Autism and site effects, and to enable the extension of our method to other neuropsychiatric conditions.