Reliable mapping of system-level individual differences is a critical first step toward precision medicine for complex disorders such as schizophrenia. Disrupted structural covariance indicates a system-level brain maturational disruption in schizophrenia. However, most studies examine structural covariance at the group level. This prevents subject-level inferences. Here, we introduce a Network Template Perturbation approach to construct individual differential structural covariance network (IDSCN) using regional gray-matter volume. IDSCN quantifies how structural covariance between two nodes in a patient deviates from the normative covariance in healthy subjects. We analyzed T1 images from 1287 subjects, including 107 first-episode (drug-naive) patients and 71 controls in the discovery datasets and established robustness in 213 first-episode (drug-naive), 294 chronic, 99 clinical high-risk patients, and 494 controls from the replication datasets. Patients with schizophrenia were highly variable in their altered structural covariance edges; the number of altered edges was related to severity of hallucinations. Despite this variability, a subset of covariance edges, including the left hippocampus-bilateral putamen/globus pallidus edges, clustered patients into two distinct subgroups with opposing changes in covariance compared to controls, and significant differences in their anxiety and depression scores. These subgroup differences were stable across all seven datasets with meaningful genetic associations and functional annotation for the affected edges. We conclude that the underlying physiology of affective symptoms in schizophrenia involves the hippocampus and putamen/pallidum, predates disease onset, and is sufficiently consistent to resolve morphological heterogeneity throughout the illness course. The two schizophrenia subgroups identified thus have implications for the nosology and clinical treatment.