Magnetic resonance imaging (MRI) has been proposed as a source of information for automatic prediction of individual diagnosis in schizophrenia. Optimal integration of data from different MRI modalities is an active area of research aimed at increasing diagnostic accuracy. Based on a sample of 96 patients with schizophrenia and a matched sample of 115 healthy controls that had undergone a single multimodal MRI session, we generated individual brain maps of gray matter vbm, 1back, and 2back levels of activation (nback fMRI), maps of amplitude of low-frequency fluctuations (resting-state fMRI), and maps of weighted global brain connectivity (resting-state fMRI). Four unimodal classifiers (Ridge, Lasso, Random Forests, and Gradient boosting) were applied to these maps to evaluate their classification accuracies. Based on the assignments made by the algorithms on test individuals, we quantified the amount of predictive information shared between maps (what we call redundancy analysis). Finally, we explored the added accuracy provided by a set of multimodal strategies that included post-classification integration based on probabilities, two-step sequential integration, and voxel-level multimodal integration through one-dimensional-convolutional neural networks (1D-CNNs). All four unimodal classifiers showed the highest test accuracies with the 2back maps (80% on average) achieving a maximum of 84% with the Lasso. Redundancy levels between brain maps were generally low (overall mean redundancy score of 0.14 in a 0–1 range), indicating that each brain map contained differential predictive information. The highest multimodal accuracy was delivered by the two-step Ridge classifier (87%) followed by the Ridge maximum and mean probability classifiers (both with 85% accuracy) and by the 1D-CNN, which achieved the same accuracy as the best unimodal classifier (84%). From these results, we conclude that from all MRI modalities evaluated task-based fMRI may be the best unimodal diagnostic option in schizophrenia. Low redundancy values point to ample potential for accuracy improvements through multimodal integration, with the two-step Ridge emerging as a suitable strategy.